A mirror-like finish on a stainless gun turns it into a scratch magnet, any little ding shows.
I prefer a brushed finish because it doesn't show dings and scratches so bad - and it's easily repairable if you do get a noticeable mark or scratch.
For a brushed finish, sand to the 400 grit wet-or-dry level - then deliberately scratch up the shiny finish with a ScotchBrite pad. Use a new one that has never touched regular steel.
If the ScotchBrite pad has been used on regular steel, it will transfer regular steel particles to the stainless, which will rust and look tacky.
Make sure the scratches all go the same direction, and are straight, not curved.
Here's a Savage bolt handle and Sleeve that I did that way, to match the action and barrel. Did the trigger guard and floorplate, too.
Click image to see it larger.