Solvent

Pretty much any penetrating oil seems to be adequate for the typical pellet barrel. WD-40 or Ballistol as mentioned above, Hoppes #9, Shooter’s Choice, Kroil, Goo-gone, etc.

I use Hoppes these days but have used most everything on the list and got satisfactory results from them all.

One of these and snug-fitting cotton patches is usually all that is needed to keep a pellet shooter clean. Contrast that with a long neglected and heavily leaded bore or choke, or a rough bore, or shooting slugs, or lead with high antimony content, or some combination thereof...something like that may need the scrubbing action of a bronze brush. It will not scratch a steel barrel, just do not use one on a brass barrel.
 
No solvent needed on my airguns! I use beeswax furniture spray on my pellets so I also use the same beeswax spray to clean my barrel as beeswax dissolves itself and causes no buildup. All natural, safe for all metals and plastics, no foul odor, great for your stock if you get some on it!! Been using this stuff for well over 30 years and never had a lead fouling issue! I also use it on my rimfire rifle with the same results..
 
According to an article written by "The Godfather of Airguns" Tom Gaylord himself, he states that we should AVOID using WD-40 in barrels because when it dries, it leaves behind a gummy film that is difficult to remove. That was an eye-opener to me !! I just recently started using that during my end-of-season barrel cleaning ritual. Will be going back to using good old fashioned Ballistol again. That's a proven product. Huh.......who would'a thunk !!