I really like Wipe Out foamy bore cleaner. One of my shooting buddies is one of the best competitive shooters in the country and he turned me on to it.
I foam up the bore, let it sit overnight, 3 dry patches. If the patches are still dirty, I'll foam it up again and run patches when I come home in the evening. Maybe one more time overnight. 3 times is the max I've needed.
On occasion I've run some more aggressive solvent through afterward, and have found no traces of anything.
2nd string of cleaner is the Hoppes copper solvent - not as aggressive as others, I use a patch and maybe a nylon brush. Again, I do it over a couple of days, running clean patches, and more solvent until I see clean patches.
Last, I have the more aggressive stuff, like Montana Extreme or Butches - I use that for more stubborn barrels. Same deal, patches and nylon brush.
I've used the super aggressive stuff, like Barns and 7.62, but after reading the directions, they scare me and I have not used them for years.