BoreSnakes and the Otis Technology pull-through system are fine for cleaning out powder fouling and oiling bores, but might be inadequate for scrubbing out stubborn copper fouling or built-up layers of plastic wad.
One-piece steel or nylon-coated steel cleaning rods are better than aluminum rods, which are more likely to break, especially at any threaded joints. Aluminum rods might harbor fine grit that can abrade bores, too. Get in the habit of wiping rods clean during each pass through a bore.
When cleaning barrels, also clean chambers. These are usually larger than bores, so you’ll need a larger brush. Attach it to a short dowel or chamber cleaning rod, wrap a patch or two around the brush and clean with solvent as you would a barrel. Use toothbrushes, picks and whatever to clean out bolt locking recesses.
Go light on oil. While it protects against rust, it also attracts dust and dirt. Too much can gum up the works. Some semiauto handguns such as 1911s shoot better “wet,” meaning lots of oil on the slide, but most others do not. And 1911s should be cleaned often to maintain function.
Screw-in choke tubes are a special case. They should be turned off and cleaned more often than barrels because carbon can build up under the threads. Moisture can also rust them. Clean thoroughly with solvent and a stiff nylon brush, then coat threads with an anti-seize grease. Screw-in style breech plugs and nipples on muzzleloaders must be similarly maintained.
An easy method for displacing moisture from all corners of a wet firearm is to heat the gun with a hair dryer, or stand it over a typical floor register. You can get gun metal too hot to touch with just a hair dryer, so use judiciously and pay attention.
Rimfire .22 Long Rifle bores rarely, if ever, need to be cleaned unless accuracy suffers from excessive carbon build-up. Semiauto actions get gummed up from powder residue quickly, which causes malfunctions in .22s.
AR-platform rifles get dirty fast and must be stripped and cleaned thoroughly to maintain function. Ditto many semiauto shotguns.