Hi, I recently dusted off my old copy of Morrowind, but I now run a Windows 7 machine. I was wondering what the best way is, from your experience, to install and run the game.

I read the FAQ at the top, and that answers problems that I haven't run into because I haven't installed the game

Well, the http://www.gamesas.com/index.php?/topic/781497-vistawindows-7-problems/ will answer all your questions and concerns.
Basically, you'll want to change the Install Location to bypass all the common problems W7 gives you.

Otherwise, you'll have to turn off your UAC. But simply moving the install is the simplest way to fix the problems that will arise.

If you you haven't installed MW on your new machine, just change the install path to Bethesda/morrowind or something like that. That should be all you have to do. If you've tried to install before, you'll have to use regedit to change the path. Don't use the default path and then move it; if there is a corruption (like the snowflake error) you'll just copy the problem to the new location.