You can get 27" tires down to 25c wide (Panaracer 27X1" comes to mind). To run it either fixed or singlespeed, redish the rear wheel (center the rim over the hub - look online), and screw on the cog. If you're running a fixed cog, buy red loctite, put it on the threads, screw it down, and mash the pedals a few times to get it on there tight. Then let it sit overnight, and you should be good. As far as chainline (very important on a fixed), check out www.sheldonbrown.com for the info.

The reason it isn't safe to run a fixed cog on a standard hub is, as said before, it runs the danger of unscrewing; however, using the method above, I've never gotten one to unscrew - including the rather loosely fitting Surly cogs. This is on a heavy steel bike with steel wheels and rather wide tires (32c) and me weighing in at 220 lbs.

EDIT: You can run 700c wheels in this frame - you may need longer reach brakes (don't run a fixed gear without at least a front brake - especially with a standard hub) to accomplish that, but on frames of this era, I'd doubt it.