Greetings,
Mr. 1. What you DON'T want to do is initiate your polishing with an abrasive (file,sandpaper,grinder) that is too aggressive initially. If you put any deep scratches in the SS it will take forever to remove them if you can at all. I recently "polished" all 85' of SS rub rail on our vessel using a die grinder and a 3M Scotchbrite (Scrulox) pad.
One has to use a light touch to avoid too many swirl marks. I
think you may achieve acceptable results if you use something like this in an electric drill if you don't have a die grinder...