I just set up a laptop with Win7 x64, as a first step in migrating away from XP.
There were very few apps I had trouble with, as long as I followed a few rules when installing them.
I created an additional folder for portable & other problem apps. If an app didn't work properly after installing them normally, I uninstalled and tried again by installing them into my extra programs folder. They usually worked well there. There were only a few exceptions, which were easily replaced. (Winzip 9's context menu integration didn't work, Panorama's installer wouldn't run, and latest installer for Opera threw a weird error about not being a valid 7zip archive, and a calculator that I will have to do some extra fussing with to get it to work) I was even able to get Delphi 6 and Paintshop Pro 7 installed and working, and those are 2 apps that have known Vista/Win7 issues.
If you are a bit nervous about Word and Excel 2002, then do the same and create your own extra folder for portable & problem programs, and install it there. My guess is that even the old Office 97 would work ok, if installed this way. (although I'd never do that, for security reasons)
And if you still can't get something to work, then just google the name of the app, version, and "win7" and you'll likely find a guide to installing it so it will work.
If you really like OE, I'd go with Windows Live Mail, as 4wd suggested. It is probably the easiest and most painless migration and will give you the successor to OE, with much less of a learning curve.
And if you like the classic theme in XP, you can have the same in Win7, except that the start menu will be different.
Explorer will take a bit of getting used to, though. No way to have that looking/acting like the one in XP.
Oh, and an extra warning related to installing Win7 on a laptop (mine is a Dell Studio). If you have trouble getting it to boot up, unplug all USB devices until after you have installed all updates, even if you have boot from usb disabled, like I did. I started having troubles after installing SP1 and had to unplug my mouse to get it to finish booting, and one of the later updates that was not included in SP1 resolved it. No more issues.