Use of Scotchbrite or similar abrasives is SPECIFICALLY advised against in the manual for cleaning the face of the cylinder. Using an abrasive in this area WILL remove metal and eventually lead to an increase in the Barrel/Cylinder gap.
What I have found to work best is to soak the parts needing cleaning in M Pro 7 solvent for 15 to 20 minutes. Then a quick brushing with a nylon toothbrush soaked with M Pro 7 will remove 80-90 % of the blackening. After that a small patch of Kleenbore's Lead Away cleaning cloths wetted with that same M Pro 7 will make removing the remainder a 5-10 minute job.
As for using the various polishes, if you use a polish frequently enough you will end up with a polished revolver. Personally, I like fully polished stainless steel revolvers so I give them a full polish when new. It's easier to clean a fully polished revolver and any stray marks can be buffed out.
However, some like the brushed look and to maintain that look will require a bit of experimenting to dull a finish that has been polished by repeated cleanings. If you don't want to do that, I would recomend that nothing more than a nylon brush and some solvent such as M Pro 7 ever be used. BTW, the Lead Away cleaning cloths contain a VERY fine abrasive so they can act like a polish over years of use. In order to restore a brushed finish it's been reported that the Gray Scotchbrite pads will produce a patter that is a close match to the original finish, however they can be a bit hard to find. Another option is wet sandpaper in an 800-1200 grit but you'll have to experiment with pressure to get a perfect match. Finally, it's CRITICAL to match the original scratch direction as closely as possible, of you go cross grain it'll look patchy.
Finally, you'll note an endorsement for M Pro 7 here. I don't work for the company that makes it and don't even hold any of their stock. The reason for my endorsement is because it is without doubt the finest solvent for cleaning a stainless gun that I've ever found and I've tried a bunch of solvents. Unfortunately at about 40 dollars a quart it's NOT cheap, however the good news is that quart will last for a year or more if you don't use more than what is needed. Hint, a light wet film is all you need, not a drenching or immersion. If it starts to dry, just give another tiny squirt and let it soak a bit more. BTW, another plus is the oder is very very mild, so no complaints about foul smelling solvents.