Start sanding in one direction with one grit, then sand in the other direction with a finer grit. IE: long ways then radius. this will help mask and flatten the lines on the surface and reduce the long lines that can occur.
Start with your 100 wet/dry, then 250, 400, 800, 1000 then 0000 steelwool.
I like to polish between grits on the polishing wheel and inspect the barrel against the light for non-polished ares and for scratches that the sandpaper and polish would not remove and re hit those ares before moving on to the next grit.
For shallow pitting the polisher can do wonders, deep pitting requires the file to be drawn and a light touch needs to be taken. If you do not have the right files get a set, just as sand paper comes in grits, files come in grades and profiles, shapes and sizes. The smaller the area the smaller the file, don't go to big of a file for a small area. If your unsure as to the filing part, go down to the hardware store and pick up a piece of bar stock or tube, about 3/4" round, scratch and ding it, and test your touch and technique on it before you work on the barrel, this way you gain some experience and gain some confidence.
Polishing the barrel in both directions also.