The the UK we use ' Brasso ' - which is actually a metal cleaner aka fine buffing compound in a solvent. That works a treat but can be smelly! Always polish from the center to the edge.

Apropos of bad CD's - if you are having trouble playing them you may have 'CD rot' - hold the CD's up with a strong light behing them (like a desk lamp) and look for holes. Some older CD's self-destruct, especially when subjected to hostile conditions - I have lost dozens like that. Nothing you can do about it . It's due to impurities in the aluminium or silver layer apparently.