The best gun cleaner supplies are those made by Hoppe. I always have a basic squirt bottle of this vinegar/peroxide mixture with me for cleaning guns. I swab the bore with this substance and let it sit overnight when I have metal deposits or stains in a pistol that are resistant to even vigorous cleaning with a bore brush and copper solvent.
Avoid using gun grease to lubricate the bore! The bore can be coated with a thicker lubricant, such as Barricade, only for long-term storage (or equivalent). Prior to firing the gun, you must clean the barrel to get rid of this!