I do, in fact, use a cotton patch over a (Hoppe's) bronze brush for everything except 22 caliber firearms. I, also, have an assortment of small toothbrushes that I use. Soaking the barrel, and other parts, overnight helps. My favorite gun cleaner? Flitz Metal Polish. (Which is chemically identical to Iosso's Bore Cleaner, and, 'Lead Away' cleaning cloths.) My favorite soak-bath solution? There are several: Kroil, Break Free, 'CLP', Automatic Transmission Fluid, or just plain kerosene.
My favorite longterm gun preservative - Especially for outside surfaces? (Ready?) FrogLube!