Tux, I'll echo what the others said. Your Varsity is in great shape. Replace the rubber, cables, and brake shoes; grease the bearings; and ride the snot out of it. It won't let you down.

Back when I was a working Schwinn mechanic, we used Quick-Glo to clean the chrome. It worked great, and it's still available: http://www.quick-glo.com/