Not to pick nits here, but if it's rusting, it's not stainless. More than likely nickel plated steel, possibly chrome plated. The corrosion on the underlying steel is breaking through the plating.

Several good methods for cleaning it have already been listed, and are probably going to give a nicer finish than the wire wheel I usually grab first. But then, the parts I'm cleaning are usually not as prominant as a coin door.

I also like the idea of a wax or polish to prevent further corrosion.