I swear buy a product called Flitz, I bought it years ago from qvc, its a blue paste and you rub on and polish off, its not messy and leaves a fantastic shine that lasts for ages, repeat polishes seem to be quicker each time after!
Its very gentle leaves a protective coating.

good on chrome, alloys, aluminium, brass, gold, silver and even on plastic to take out scratches, my old mobile looks brand new.
I would not use anything else.