Use the tips in safe computing as a start, but here are some additional tips.

You can change the location where you save your email on your PC:

Under OE -> options -> maintenance, select location.
You can also find the backup of your entire OE database and transfer it onto another machine:
In your existing machine, under OE:
file -> compact folders find directory in c:\Documents and Settings\"PC Login ID"\Local Settings\Application Data\Identities\"Key"\Microsoft\Outlook Express\
You will have to go into the Identities directory to ID which one is the correct one if you have munged OE in the past and created other identities under your PC login. Copy this entire directory to the same directory on another machine, logged in as the user you want to be. OE should pick it up. Even before you create the email account. 

You can also try tools -> options ->maintenance -> "store folder" to see where your OE folder is. You can copy this entire folder to another location to save your email. 

Here is a good site describing OE backup procedures. This describes how to restore OE.  Here is another good source on backing up and recover your OE Data  http://support.microsoft.com/default.aspx?scid=kb;EN-US;q27060 

Here is some good advice, also repeated here email advice...

As you are all becoming aware, email can be a very non secure form of communication. Make sure you understand the following:

1) The FROM address can always be easily forged in current email clients. Only in the header can you see any "real" stuff and this can be very difficult to decipher.
2) You may be on a BCC list, which is why the TO address is not yours, but you still receive it. I would be suspicious of this.
3) Anything you say in an email is clear text and is liable for interception.
4) Only if you keep your Windows software up to date, the antivirus up to date, lock down IE and OE, be vigilant about spyware, and stay away from malware sites, are you capable of keeping ahead of the miscreants and terrorists in Internet space. The default manner in which Microsoft has bundled their email client has probably done more to encourage/allow hacking than anything else, except the actual vulnerabilities of Windows itself. Only with SP2 on XP have they actually defaulted the application to a safe install!
5) MACs and Linux are still less vulnerable than Windows, but there are ways to get to them too.
6) Older versions of Windows are especially vulnerable, doubly so if not kept up to date. You can still update Windows 98 and ME. Although Microsoft is maintaining the update capability for them, it is NOT backhauling the security pecautions into them that it is putting into XP.

I am recommending the following to many people:

1) If you are using OE and IE, then you should lock them down, at least on your main PC where you have all your tax returns, investing stuff, any other private stuff. Steps for doing this are on my web site. This can be a pain. On my main PC, I punch a LOT of popups denying ActiveX and scripting. But I feel more secure!
2) I would consider switching from IE to Mozilla firefox. It is a terrific browser, very similar to IE and not yet susceptible to Windows vulnerabilities.  When you install, it pulls all of your settings from IE. You can elect to NOT make it the default browser until you get used to it. However, it looks very similar. And you will like the tabbed browsing. And the popup blocking.
3) I would also consider switching from OE to Mozilla Thunderbird.  When you install, it pulls all of your settings from OE. You don't have to worry about setting it up. It blocks images/attachments by defaults, and has an easy override button if you know you want to do it anyway. This is a really nice email client... so far as I have looked at it.
4) Make sure you upgrade to XP SP2 if you have XP. Especially if you are NOT behind a router of any kind, or you are on dialup. [shame on you...]
5) I would spring for a new PC this Christmas if you are getting really tired of this stuff. It will usually have XP, and it will likely come with an OEM version of XP SP2, even better. I might even suggest a MAC, because it has evolved to UNIX underneath the hood now, and even has a command line. It is quite different from the Windows way of doing things, and will take some getting used to. But I wouldn't doubt that they still charge twice as much as Windows boxes. I am sure Ellen and Niel would give advice in this subject.
6) If you are adventuresome, Fedora Linux is FREE and you can do everything and then some with it that you can do with Windows and MAC. It can be installed on any X86 Windows box, but not, in general on a MAC box. I have been using Firefox and Thunderbird on several of my PCs, and I really like them. They are free of course. You can use them at the same time you use IE and OE. Glor has been trying them as well. She can give you some idea how they look. The down side to Firefox and Thunderbird are that you have to keep them up to date out of the Windows context. Firefox does have a built-in update notifier, and the update is quite easy. Good for them.
7) There is a secure way to do email, and it is already built into all the popular email clients. I have tried it and it is not too difficult. It involves buying a "digital certificate" from websites like Verisign which you attach to your email. Recipients can then verify the email is from you using a second key generated by Verisign. This "Public Key Infrastructure" is used in all kinds of ways, but just not in universal email. They are free ways of doing all this, but not quite as straightforward. I discuss this here.  Using this technique of using "certificates" you can insure the following: 1) You can verify that an email is FROM the person whom you think it is from. 2) You can also encrypt the body of the communications to make it readable only by the person to whom it is sent.

Here are some tips I shared with some family members:

1) actual size of photo - this is usually the most important when you are considering speed and delay. You should look at properties of the file before you send it. If it is over 100KB or so, it will take a much longer time to rcv (and send) on a dialup connection. jpegs of reasonable size and resolution are usually less than this, unless you send huge pictures with huge resolutions, like Ellen usually does :-). When you adjust your digital camera for higher resolution, the bigger they are.... bmps are usually humongous, should never be sent. TIFF files are usually huge also. Not familiar with others.
2) Some people use free web mail (hotmail, yahoo, the like), where their ISP storage space is severely limited, maybe a few MB - they don't use an email client which runs on their PC. Some people have 10 MB web space. Mail is stored here until you look at it using webmail (your browser), or your email client goes and gets it. A lot of time this fills up with spam. You don't really have to run an email client if you want - you can choose to always use the webmail, but you always have the maximum storage issue. If you see a picture on the webmail, you can right click and save image. Note that this involves a download to your PC, so wait again if you're on dialup. Many people have problems with their email downloads freezing. Your antivirus may be choking on this. You need to go to your webmail and delete/edit your emails before they get downloaded by an email client.
3) If you leave your PC on (ADSL or cable modem) and connected, you don't have to worry about mailbox size, IF you run your email client all the time, and set to periodically retrieve email.
4) mail is mail, when you send or get your mail, it all goes/comes at once. There is nothing you can do to break up a single email. [you can actually go to the webmail (browser pointed at your email while it is still on your ISP instead of your email client) to preview who it is from before downloading it - this is usually good practice if you have dialup and people keep sending you humongous files]. But if you choose to open a picture that is sitting on your webmail, it still has to download the picture to your PC so an app there can open it - even if the email is still on the ISP.. SO wait again....
5) The only thing you can usually set on the tmt side is text or html. I don't believe anything you set on the tmt side has anything to do with how a rcv views the email, except for this. If you select text, then anything not text is attached. It all goes at ONCE when you push the send button. And it all comes at once on the rcv side. It is a single piece of email, no matter how many attachments there are. [I do notice in OE a "send pictures with messages" option in the html settings of html email - not sure what this means....]
6) on the rcv side you can normally set your client to receive text only, in which case, non txt stuff should not expand in-line. It should show as attachments. But most people can't stand to rcv txt only email. If you set to receive html, then it ..may.. be in-line. This seems to be the question, but it ALWAYS downloads the email, and you have to wait anyway if you are on dialup. But in this case, just turn preview mode OFF [on OE you can add the PREVIEW button to the buttons on top]. The mail is still downloaded to your
PC, but the email is not displayed until you click the PREVIEW button. This is one of the best things you can do to prevent ActiveX and javascript bugs in spam from "catching" you. [In the OE security tab there is a "don't allow attachments to be saved or opened that could be potentially be a virus" - I think this watches for vbs files, or word macros]
7) In OE, when the email shows up in the rcv panel, it is already SAVED in OE's big file, including the attachments. You can move it to the delete folder, or a special folder if you want. You don't have to do anything special to save it.
This is still all very confusing. But if you are on a dialup, anytime people start sending large files around, the people on dialup just have to wait for the files, unless they are using webmail, in which case they can preview who it is from. If they choose to look at a picture, then you still have the delay.
8) If anybody is running Outlook as opposed to OE, then this works totally different, especially in a corporate environment where you are using Exchange servers. The email is always on the server, NOT your PC. But you can setup Outlook to run like OE if you are using it for a simple POP3/SMTP email client.
9) If you are running an IMAP email client, this can work totally different as well. I think OE only does POP3/SMTP.
10) There are different options about encoding non txt in MIME standards, which you can actually play with deep in the settings, so there may be some differences in how the clients view/open the different encodings.

Clear as mud, huh? Basically if you are on dialup, you have to wait around at some point when you are dealing with a large file.... previewing, getting, sending. Just no getting around it.

If you want "final" clarification.... :-)

If you want to read the actual standard (RFC) protocol governing how your email client gets email from an email (POP3) server, here it is. It is actually not too hard to read - try it!! http://www.faqs.org/rfcs/rfc1939.html

Notice this line:
POP3 is not intended to provide extensive manipulation operations of
mail on the server; normally, mail is downloaded and then deleted. A
more advanced (and complex) protocol, IMAP4, is discussed in.....

And this one:
When these facilities are used in this way by casual users, there has
been a tendency for already-read messages to accumulate on the server
without bound. This is clearly an undesirable behavior pattern from
the standpoint of the server operator. This situation is aggravated
by the fact that the limited capabilities of the POP3 do not permit
efficient handling of mail drops which have hundreds or thousands of
messages.

"Already read msgs" result from your running an email client on many different machines, like I do, but only DELETING the message (email) -at the server after RETRIEVING on the one PC where you keep your email. You may notice that this is a pain if you read your email on one PC, and then you go read it from another one, and it is NOT there to retrieve. So you set all email clients except your main one to "leave msg on server." [This doesn't apply to webmail, only clients on PCs]

There are only 13 possible commands a client can issue. 10 required, and 3 optional. The RETR command gets the entire set of msgs (emails) after authenticating (giving the server your username/passwd). This is the normal request from the client. I do see an optional "TOP" command that can be issued by the client to look at so many lines of the message (email). This would mean your client does NOT download the entire message, just the "header" plus so many lines of the body. SO.... the question is do any of your clients implement this optional command. It would probably be done by a "retrieve header" option or something similar. I don't see anything like this in OE, tho there are some strange wordings in some of the options. You need to dig into your options and see if you can find this command which probably handles the TOP cmd. And then set it to retrieve header if you only want to look at TOP of email. Presumably if you delete the TOP of the email, the client will issue a command to delete the remaining part of email on the server. You would think so, wouldn't you. You can actually bypass your email client and speak POP3 directly to your ISP server if you like. You can use the TOP command here if your client does not do it. This shows you how.  For further clarification...

Here is the standard for the format of the email messages.   And here is the standard that your client must meet for delivering these email messages to an SMTP server (POP3 only GETS email from a server).  So there you go. Write your own client if you want.... You only need to learn how to speak POP3, which is pretty simple. Clear as mud, as usual... But the RFC standards can actually be understood with a little reading. Your email clients just implement these standards.

Even the Feds are finally getting into the act.  Here is some advice from the FTC.

Here are some comments from Fred Langa's LangaLetter

Hi Fred. I have seen this quite often with my clients. 99% of
the time their mailbox on the server will contain an email
with a several megabyte attachment. When they check their mail
the normal messages that are in the queue before the large one
are downloaded in the usual manner. The server will then churn
away gradually delivering the monster. Sometimes the
connection will time out or will drop before delivery is
complete, but usually the user will misinterpret the seemingly
lack of progress as a hang and will cancel the request. They
will then try again and the same thing will happen thus
receiving multiple copies of those messages they have already
downloaded. Until the server receives conformation that all
messages in the queue have been delivered it will assume that
none have. Email servers were not designed to handle
multimegabyte files. Most ISPs have web browser based "Hotmail
style" email access that their clients can use to access their
accounts from any internet connected machine. If the problem
is being caused by a large file, this interface can be used to
read or delete it without downloading. If it is a file that is
important then the client should try downloading the mail
again and while this is happening go have a coffee, read the
newspaper and perhaps have a small nap. Multimegabyte emails
can take quite some time to download especially with a busy
mailserver and a slow internet connection. If the above does
not work then call your ISP. ----
Terry Harris: Fred, I work for a regional ISP in Central California, and
"Email Deja Vu" is an all-too common problem. One thing we
find very frequently when an email "hangs" during transfer
from the server is that the email has an attachment. If your
ISP offers a webmail portal for accessing the email server
through a web browser, you can see which emails are hanging
up, and determine if it is worth the effort to download them,
or just delete that joke which has already been forwarded to
you five times in the last month (Dad, are you paying
attention here?!?). If the attachment is a photo that you
would like to keep, you can always right-click on the image
and "Save As..." As always, Fred, thank you for putting out
the best Windows newsletter around. The Plus subscription is a
fantastic deal! --- David Burrows

Hey Fred. If he checks his email with a website like this,
then it will allow him to delete
individual messages from the server and fix the problem
himself. Also he will be able to see who the message is from
and possibly a little of the message as well to know if it
might be something important. I know I have a recurring
problem with a certain family member that sends very large
picture files through the email clogging up my own inbox. As
well if it happens to him again, then he can clear up the
problem on his own without having to call the ISP. There are
other similar websites that do the same thing but this is the
one that comes to mind. It is also pretty straightforward. All
you have to do is type in your email address and password. I
love the newsletter. Keep it up. Thanks! ---Matthew Lewis

Fred: I had this problem with the scanning function of Norton
Antivirus. Any time I was sent an attachment over 1 meg, NA
seemed to choke on it. I would wait and wait and it would
never download. I would have to use a program called Mail
Washer to delete that file off the mail server so I could get
my mail. This went on for weeks. I finally got tired of it and
started changing various things on my system. Nothing worked
until I turned off the option to have my incoming mail scanned
for viruses. I experimented with it using a test email several
times and that turned out to be my problem. When Roger logs
off, the mail server hasn't updated the "received" flag yet,
so all the emails would come down again. As soon as they do, I
believe that NA chokes again on #7. I don't think this is an
unsafe practice because I have NA running in auto-protect
anyways. If I open anything that could be a virus, NA would
jump on it then. I hope this helps. Love the newsletter.---
Patrick.