I have an 89 Trek 660 that I built up as a fixed gear. Wonderful bike but with one tiny caveat. Later Trek steel frames (I'm guessing mid-80s) have house forged dropouts that are probably 3mm shorter than the classic Cinelli dropouts pictured above. Which means you are slightly limited in your gearing choices. Not a huge deal, but if you're using a flip-flop hub, you may be able to have only 1 or 2 tooth differences.

Edit:

Here's a picture: