That's right. Work backwards through the grits from fine to coarse until you get the scratches out, then work back up, feathering out over the edge of the last grit. I don't use a polish for anything other than high-gloss, but I would use red scotchbrite with water. Then gray scotchbrite if the finish warranted it.
If you polish to a high gloss, get some stanchions and velvet ropes and barricade the sink area off from the rest of the world. Even looking at it too closely will scratch it.