All the previous poster's have good advice, but here's some of the products I have tried lately,
Gunslick foaming bore cleaner, Id rate this product as a # 7, on a scale of one through ten.
Shooter's choice "copper and lead remover" it only get s a #6.
Barnes Copper remover, gets a #7 also.
Smith&Wesson Bore gel gets a #7 too.
Hoppes # 9 gets a solid five, because it does run the Girls plumb out of the house!!
Butch's Bore shine would get a #7 but all the braggs and hype didn'y help this product work right, it only gets a #6
Break free CLP is going to get a Soid #8 because it's a product that will smoke any carbon build up,,
(and you can rinse it off in hot water).
I also use a Non-chlorinated brake cleaner spray to remove any loose grease, grit and "what have ya".
P.S. I only use Naphta (lighter fluid) on my trigger systems, about once every three trips to the range,,, and blow them out with compressed air.
I also at this very minut trying my lateset purchase Boretechs Eliminator,,, juries still out with this one.
Last and certainly not least I take a spray can of G-96 ceaner lube and protectant and spray the entire action and I blow it out with an air compressor to remove excess oil, and wipe down all metal parts with the stuff, it removes carbon very nicely but is a little soft on the copper residues.
Since it does have a pleasant smell and outlasts any other CLP product, I'd give it a #8!! Every gun care kits is barren without this product!!
Hope this helps!!! ( you don'y want to know how much I spend on my gun maintenance)