When shooting a lot of trap, I used WD40 (gasp from the crowd.)
Hose down the barrel liberally, scrub with a brush, push a wad of paper towel through, and watch the dissolved wad plastic run out like warm syrup.
With an OU, brush everything else to remove fouling and, as the old knife ad said, "oil the joints." Not with WD40, of course.
For my 1100, dry brush the gas system, wipe off the loosened carbon, and reassemble. Occasionally lightly lube the action.