Thanks to all.
I think I'll try a couple of the suggested methods on another old bike, one I'm not too concerned about, before I go to work on polishing the Varsity. It looks like this bike was stored in a garage for the last 30 years because the rust on it is not so bad. Fortunately, I'm in New Mexico where there's no humidity, so whatever rust I do rub off will take a long, long, long time to return.
I appreciate all the advice.
Sprayman