First I only clean the BORE every two or three range sessions. Use a non PTFE based gun cleaner. Not Breakfree CLP. Preferably something that is a powder solvent only.
Then, only when group size increases, a copper solvent like Sweets used EXACTLY as reccomended. Don't use for regular cleaning. A foaming bore cleaner would be a second choice.
Some people swear by JB bore paste. It is a mild abrasive. Only use if the above did not get everything. Don't use for regular cleaning. Perhaps once or twice during the life of tbe barrel.
Use a bore guide. Use a quality, coated, non segmented cleaning rod. This will eliminate big errors scratching your throat or bore.
For an AR15, I only use a bore snake to get crap that a chamber brush got into the throat. Use a powder solvent or gun oil on the bore snake. Only do 1 pass at the end of chamber cleaning if you use it at all. I don't use one on bolt guns.
If you strip the copper fouling from a barrel it will take 5-20 rounds to settle back down. If you just clean powder fouling, it will take 1-5 rounds to settle down.
For this reason, I often do not clean the barrel or only clean the chamber and do a single pass with a boresnake. Then fire 1 round to clear the bore. This limits cold bore shot differences.
Over/impropper cleaning ruins more barrels than wear. More barrel life is wasted if you completely strip the gun to zero copper and have to shoot 20 rounds to get it to settle back down.
Just one perspective. Others will have different opinions.