I wouldn't buff it - at least not initially. I would suggest hand rubbing it with wet/dry paper, on a piece of steel or hardwood, starting with 220 grit and working my way up through at least 400 grit. If you work one grit until all the scratches are going the same way, then change direction with a finer grit until all the scratches go in the new direction, you can get a pretty highly polished surface without a lot of rounding off or dishing out. If you want a real mirror polish, go up to 1000 grit and only when there are no scratches showing at all, hit it lightly with some fine buffing compound.
By the way, if you are using a buffing wheel, be careful. They sure like to snatch a blade out of your hand and stick it in your leg, or the wall across the room. I'd rather not tell you how I learned that.