I done that job on my last car.... tedious but enjoyable lol
Granted, I sprayed them too but the surface under the new paint was much better anyway.
Not saying this is the correct way, but it worked for me.
Clean calipers down with wheel brush to get heavy shite off.
Wire wool also, good stuff to be fair.
Used 2 products, Bilt Hamber Iron Fallout Remover, let it soak for a good bit, but not dry on
Rinse
Then an Autoglym All Purpose Cleaner mixed fairly strong (1:4 I think? Maybe 1:3, can't remember...)
Rinse
Repeat again if needed
I got mine down to a fairly good silvery finish with this, smooth too with the wire wool, they were not perfect, but I was spraying as I said so it wasn't an issue, but I'm sure with enough elbow grease you could get them looking A1
If that fails, you could take them off and get them blasted, but you will probably need new seals and pistons and what not to be safe afterwards in case any sand or glass beads got into those areas
Got that done also before, think was 80 for the blasting