I use an automotive chrome wheel cleaner made by Mother's . It sprays on , let it sit a bit , I use a wire brush ( brass preferred ) and rinse off . I've taken some hopeless looking chrome pieces and was amazed how well they cleaned up . ( No , I don't sell the stuff ! )
They also have a similar aluminum cleaner that I have used on engine cases and hubs that also does a great job that should be included in another post as a better alternative to sand blasting .
But yeah to the other stuff . I also use this kind of wadding in a can . Never Dull is the brand I have , but have seen it go by different names . Non abrasive means is best IMHO