I start with a mill file. Leave enough extra material after the coarse filing to be able to fine file and sand all the file marks out without making it below the level of the main frame.
Then draw file with a relatively fine flat file using chalk in the teeth to prevent galling (gouging) works best especially on SS and brass since they are both relatively soft, a lot like filing aluminum alloy.
Then flat sand with a true flat surface small metal sanding block starting with 400, then 600, then 800. If you use 1200 then 2000 grit, the finer the grit you end up with, you can just polish to a shine and no buffing needed And therefore no risk of rounding the edges. Go slow and check fit to main frame often! And also to your grips for a perfect fit. Stop sanding after using the 600 or 800 grit paper to match the finish on the gun or leave a sheen.
You won’t need to do the entire surface of the grip frame with the same grit progression since the grip frame as it comes is pretty finished in most areas. For curved surfaces like the backstrap, trigger guard etc.; use crocus cloth like a shoe shine rag and a 1” x ¼” x 2” eraser for your sanding block to avoid leaving flattened areas. It will conform to the curved surfaces.
You may decide to stop with the grit that most closely matches a satin finish. If you decide on a high gloss finish you'll need to buff slightly after the 2000 grit.
Hope this is helpful,