Several stainless polish compounds are available, along with automotive paint cleaner products (which will also work on stainless.
(Try an auto body paint supply store for buffer & polish materials)
You will probably need to experiment a little, based on the degree of oxidation you're dealing with. Start with a a very fine polish & then go heavier as needed.
I generally use a variable speed commercial buffer & wool pad. Anything less will work you to death (unless you just need the exercise)