I agree with getting a good one piece cleaning rod. Either wood or one that's coated.
There's plenty of chemicals out there to chose from. Sort of like picking the best oil for your engine. Try them all and pick the one you like the best.
The Marine Corps was very **** about cleaning our weapons. Inspections were with toothpicks and white clothe. Anything at all was enough to fail.
Automotive brake cleaner that you spray from a can cuts through oil and grease better than anything I've ever come across.
Some competive shooters I know say to only run a brush down a barrel the same direction the bullet travels. I make sure to push it all the way through before pulling it back up. No half strokes!!!
After the brush, I put the patch over the brush and put it down the barrel. Then I turn it over and use it again. I do this until it comes out clean. I also go through allot of patches!!!
I lubricate very lightly and plug the barrell with a few patches rolled together.
After cleaning, I know the first shot is gonna be off, so I take a few without really aiming. Then I'll check my group with three shots from a cold barrel. After each shot, I let the barrel cool. A hot barrel shoots different than a cold one.
I saw a guy at the range with four boxes of shells. His first couple of groups were all over the place, but then as his barrel heated up, his groups closed in. His second, third and fourth boxes of shells were all very well grouped. I asked about it and he said his gun shot better hot. He was pretty cocky and annoyed me, so I droped it and left. But to this day I wonder if he's ever killed anything with his first dozen shots while out hunting with a cold barrel.
Eddie