Some guys use oxalic acid, CLR, Bar Keepers friend, auto chrome polish, naval jelly, Noxon, Brasso, motor oil and fine steel wool, or just a wet and soapy Brillo pad on the chrome parts. Best to use steel wool as a last resort, since it scuffs up the finish. Auto engine degreasers (ex., Gunk) can remove the greasy old grime...be careful if using gasoline, and not indoors. An old rusty Varsity, however, may be a good candidate for a wash down from a garden hose, followed by a soapy scrubbing with a Brillo pad. For the painted areas try an auto cleaner wax, or a light duty auto polishing compound. BTW, old Chicago Schwinn's are nearly indestructible. Good luck with it.