To the basics, understand that you have carbon fouling, which is the black sooty residue you're probably thinking about...
And copper fouling, which is all the slough-off of the copper jacketed cases that builds up in the bore from the bullets cutting their way through the rifling.
Some cleaners remove both, some only one, or the other.
Hoppes #9, has been used for decades for powder fouling, but does not remove copper.
There are many new "modern" products, and everyone will say theirs is the best.
I still use Hoppes, to clean internal parts...
I never liked the idea of running brushes down my bores, so now I use only Wipe-Out. Removes powder and copper fouling more than any other product I've ever used, and is the easiest to use on top of it all. Spray it in, leave it soak overnight, patch it out. DONE.
It even leaves a protective film against corrosion in the bore.
http://www.chuckhawks.com/wipe-out.htm
http://www.paulcompany.com/wipeout.htm