BB guns aren't very good for real target shooting. They'll never be that accurate, barrels can wear more quickly, and the steel BBs themselves will ricochet dangerously off any hard surface. Pellet guns are the way to go. Daisy's made the model 953/853/753 for decades as an entry-level match gun. Really common with youth shooting clubs and things like that. They're really cheap used. It's strictly a target gun so get something else for pest hunting.
I was really into air guns for a while in the 2000s. Had a single-stroke 10M competition rifle that was a lot of fun. Eventually kinda migrated away from the hobby, but I still have a couple. Older Beeman P1 pistol and R7 rifle. Basic target springers made by Weihrauch in Germany.