My polishing is all done manually without machines (so far at least). I have a great extra slim triangular taper file (possibly diamond coated) that is used for harsh gouges, etc. and it does not leave marks behind which cannot be removed with fine sandpaper.
I used to start with 300 grit and then 600, etc but lately have been trying to start with the file and 1000 grit. I find it easier to avoid fine scratches left behind by the coarser grit sandpaper. I also sand mostly wet and seldom dry going in 500 grit increments up to 3000 from 1000.
The 3M 3000 grit polishing sandpaper is a good product, it's like a super thin paper/sponge and it lasts a long time, used wet and then rinsed out and dried. Once sanding is finished I use Mothers Mag & Aluminum polish with cotton balls (I read somewhere they were a good choice and they seem to do a good job).
Lot's of elbow grease for sure