Im with the other guys that suggest a 22lr bolt action, or a 223 bolt action.
Probably start with the 22lr, put a few thousand rounds through it, then step up the cartridge, and distance.
Only suggest the 223 for price and availability. Can always add more rifles afterwards if your planning on hunting big game. Or just make the leap from 22lr to something larger than 223. I'm a huge fan of the newer 6mmARC or 6.5 Grendel for new shooter. Not much more recoil than a 223, but is better at catching you some game.