You can always try and buy a fixie on Craigslist or Ebay. I got my Jamis on Ebay for a couple hundred bucks. Then I tweaked it a little to my liking. I know its not the true hipster way but I probably saved over $500 in the end, plus the frame is ridiculously light.
Any frame will work, but some frames carry greater risks. Whatever you choose, use track lugs and tighten them good. The main issue is chain tension. I have lost my chain while riding, when I had a Fuji Royale frame, and it is not so good. You have to throw your heel into the back wheel against the seat stays, unless you have hand brakes. I was living in Minneapolis at the time and the traffic was tame, i.e not Chicago traffic. If you are serious about a fixed gear set up invest in a track frame. Otherwise, take your chances. Start out with a low ratio: 42/16 or 48/18. Just my advice. Use hand breaks too.
I guess if you want to get technical about it you could convert any frame and have it 'work' but in all reality not any frame will work if you want to build a nice, safe, bike that ends up being a reasonable value.
Vertical dropouts and fixed gear have no place together because there is no way to set the proper chain tension and you can not safely run a chain tensioner.
Look for horizontal drop outs and decent construction and you can find stuff all over the place.