Welcome to the makers section of BF
I hand polish my blades so it may not be quite the shine you want (not like some mirror finish) but one of my 1500 or 2000 grit finishes comes pretty close. A mirror polish requires the use of a buffer... that's the most dangerous machine in a maker's shop and to be honest, I'm afraid of buffing blades.
The secret to a good metal polish is the same as on your bows, a good foundation. Can't get a pretty shine on rough wood, same applies to metal. You want to make sure your metal is flat or uniformly curved if it's a hollow or convex grind.
You have to make sure every scratch from the previous grit is gone before moving to a higher grit. A 60x scratch will always wait until 1000x to show itself

I use dykem or magic markers to color the blade so I can see where I'm removing metal and make sure that I change directions when I change grit. So all the coarser scratches should, I say "should" be gone when the dykem/marker is gone and all the scratches from the different direction are erased.
I usually hand sand from 220 or 400 to 600-2000 depending on how the knife is to be used or customer preference. I finish on my grinder with a 400x cork belt loaded with green polishing compound. Usually I can go straight to 400 from there (probably go 600 but I do like to hand polish lol) I use 3m sandpaper with water up to 600x. I don't try to get every single bit of use out of the paper, if I think it's not cutting, I toss it. 600x on up I use baby oil as a lube, there's a saying, "water cuts, oil polishes." Yes, I do a 600x with water and a 600x with oil. It does make a difference.
The last grit is done using a "straight pull" instead of back and forth to prevent j-hooks and to keep the lines straight. The last couple of sanding strokes are done dry, just seems to leave a cleaner finish at the end.
I use some sanding blocks made of 1/4" micarta. I use the 1/4" side to do my polishing, I find it helps keep my sanding cleaner and I get a little more pressure that way. I have a block with leather on it for convex blades.
I hope this helps. By the way, what's your name? If you'd add it your sig line we could call you something other than Archer, unless Archer is your name....
