What are you attempting to achieve. Are you referring to a nickel, stainless, blued or what type of finish is the barrel.
For a very light polishing I like Mothers Billet Polish. It is less aggressive than Mothers Mag Polish, and others like Wenol, Simichrome Posish or others. The pad you use can also affect the aggressiviness. Light application pad would be cotton, sligtly more aggressive is Shurhold Ultra Fine brass wool pads, and then on up to 0000 steel wool.
Then follow it up with a coat of Renaissance Micro-Crystalline wax polish to protect the final finish.
If you are attempting to remove bluing, then simple soak the barrel in a 50/50 mix of white vinegar and water. It will remove all the bluing in a couple of hours or less.