I use a quality stainless steel rod with a brass rod guide. You start the patch or brush into the muzzle, then get the rod guide centered into the muzzle to protect the crown. haven't had any trouble in over 30 years using this method.
Alternate method is to use one of the pull trough kits from Otis or others.
Additional essentials for revolver cleaning-M7-Pro is a very good modern, low odor cleaner which really seems to lift fouling better than the new formula Hoppe's No. 9.
If you shoot lead projectiles, the COPPER Chore-Boy is a superb leading remover. You just wrap some strands around a used bore brush, dribble solvent on it and scrub the lead out. On thing-make sure they are the solid copper Chore-Boy, not the more often seen copper washed steel! Those will ruin your barrel.
Any good, light modern gun oil will do for lube, even a 5w20, or 5W30 synthetic motor oil, though I stick with gun oils.