I converted a 1984 fuji recently, you can read my buildup here.

I totally agree with the others about going to 700 wheels, and ditching the 27's. The biggest reason being that you'll have a much larger selection of tires to choose from. For what its worth my stock brake calipers reach just fine (in front, I never tried the rear).

The advice about "don't use the frame" is BS; IMHO the bike snobbery on this forum is out of control. Sheldon brown puts the smack down here regarding track frames on the road.

However, if you want to be riding fixed as cheaply as possible just go to bikesdirect and get a Windsor for $300. If you do your conversion properly you will almost certainly spend well over $400. After all was said and done my Fuji was roughly $500, and I didn't spend crazy money on anodized testicles like so many of the excessive bikes you see on here.

Jeremy