I just finished my first fixed-gear build. I opted to buy a new wheelset specifically for fixed gear - Weinmann DP18's with a flip-flop rear hub. They may still be on sale at Velomine for $99. This purchase saved me re-dishing my old wheel (which was a piece of rusty steel junk anyway) and ending up with a potentially dangerous bike that could lose the track cog while I'm riding. Also, it turned out that the 51T chainring on my original crankset was perfectly aligned with the track cog - no shimming needed. All in all, any easy build yet still reasonable. I don't know about finding a rear wheel for $60, but a anything is possible on Craigslist or Ebay.

Good luck with your build!