Make sure to add some WD40 or water to the sandpaper, it smooths out the finish with the sandpaper compared to dry in my opinion. I'd start with 1000 and then 1500. You can go higher if you want, it will only help. Once the sanding is done, get some fine polishing compound/paste, apply it to a microfiber towel or a polishing specific pad and clean it up until it shines. I've had great results with that method and SS.