Read that Sheldon Brown page about fixed gear road conversions. It's still the way to go, in my opinion.
This past summer I converted a nice old Miyata 512. Found it on Craigslist, and got a decent discount, as the rear wheel had cracks around most the eyelets from someone overtensioning the spokes (I wasn't going to use it anyway). Altogether, I might have $600 in it.
I got a new set of wheels, rear cog (3/32") & lockring, shorter chainring bolts, longer rear axle (Wheels Mfg) & some rear axle spacers (glorified washers). Mostly I removed things: second bottle cage, front & rear derailers, shifters, rear brake, smaller chainring.
The only local shop that did fixed gear stuff closed a year ago, so
I ordered most parts from Retrogression. I also got a new saddle, bar tape, brake pads from my local shop. (The saddle was 1/4 the budget...)
I like it a lot. It definitely rekindled my interest.
In addition to that Sheldon Brown page, the site
surplace.fr has a useful gear calculator.