Depending on what you are starting with as far as damage goes, you can start with 220 but that's pretty coarse. You might want to start with green jewelers rouge on a buffing wheel. Black rouge is more coarse than green. Wet and dry sand paper used with water works good but the stainless kicks the crap out of it so change your paper often. Once you've determined how bad the scratches are that you want gone, you work your way from coarse grits to finer grits. You might find that you need to start at 220, and if so, then go 400, 600, 800, 100, 1200, 1500, 2000 then rouge. I researched (like you are) because I knew nothing about it and decided to tackle it. The process is very time consuming, mind numbing at times and nerve racking too when the buffer is spinning like mad and you are working on a curved piece... cross the wheel with your piece of stainless and it will turn into a pretzel in a nano second! The pictures below show steps from a hole being welded shut, then the different stages up to polished. Good luck!
