Sounds like you want a .223. Plenty ammo available. Enough recoil in a bolt gun to make a young man smile but no so much that it hurts. .17 HMR can be lots of fun. About the same recoil as .22 LR if you can call it recoil. Shoots much flatter than .22 LR and it isn't hard to find a reasonable priced rifle. Savage makes nice bolt actions. Don't know how old the kids are but 30-06 can carry a punch and ammo isn't what I call cheep. Reloading my own I send about $0.50 + down range every time I pull the trigger.
Guns are not dangerous! People are! RKBA!