The Chore Boy (which is 100% copper and not copper plated steel as some others are, so use a magnet to check before you buy) and the Big 4 Metal Cleaner pads work, as do the Lewis bronze patch devices.
The best way to use those is get the bore good and wet with PB Blaster or Kroil the day before you use them. Those super penetraters get between the layers of lead where the carbon separates them and makes them easier to brush out by any mechanical method.
There is also now a lead solvent by the makers of Wipe Out, called No-Lead
The advice to add Lee Liquid Alox or (less expensive) White Label Xlox to the bullets is good.
I don't know what kind of gun you are shooting, but if it is a self-loader, try seating your bullets out so far that when you drop a cartridge into the barrel, the case is flush with the breech end of it. This way you are headspacing on the bullet, which I find both improves accuracy and reduces leading significantly. The only limitation is some guns won't let you do that with all bullet shapes before they cease to fit the magazine or feed reliably, so you'd have to try it on your gun.
If you have a revolver, you need to slug the chambers to be sure they are a minimum of half a thousandth wider than the groove diameter of your gun. Meister Bullets makes what looks to be a good slugging kit
if you are unfamiliar with the process (but get a micrometer
that reads ten thousandths, and don't try to get away with using a caliper for the measurements)? You also need to slug to be sure you have no constrictions in the bore? They are common in revolvers where the barrel screws into the frame. They are also common in lever rifles where dovetails are cut for sights or for the forward magazine tube mount. Constrictions cause massive leading, be they in the bore or at the chamber throat. Firelapping will clear them. Alternatively, cylinders can be reamed