Originally Posted by vw_thing

Easy conversion: pull the derailleurs (you have semi-horizontal dropouts), swap on a single speed (BMX) freewheel and chain, and pick which sprocket you want. I'd suggest swapping out the rear axle with one that can accept track nuts. Otherwise you'll want to stuff the axle as far as possible into the dropout and clamp the QR down hard.

For the rust, it depends on how bad it is (pictures might help). If it isn't wide spread, I'd probably get a cheap ($10-$15) quart of touch up paint matched by a local store. Sand the area down (you have thick tubing) and carefully blend it in with a small brush. If the rust is all over the place, it isn't really worth trying to save. The Varsity, Collegiate, and Continental were not exceptional bikes to start with, and time has not done anything for them. Still, I think they are interesting pieces of American cycling history, made in Chicago by a unique manufacturing process ("electro-forging").

Don't start making hipster cuts on that frame (removing the cable stays). Chances are you'll either find out SS is not for you or you'll get hooked and want something lighter and nicer riding. Either way, the Schwinn makes a better novelty 10 speed than a serious SS/FG bike. Most of the components are at least decent quality - those not made in the US are Japanese or Swiss, no Chinese crap.

Bottom line: don't drop serious money into it, just make it safe and have fun.