I have taken a lot of small game with my Winchester 1000X pellet rifle. Its rated range is 300 yards, but with with my middle-aged eyesight and Copperhead .177 cal pointed hunting pellets, I limit my shots and easily take rabbits at 50-75 yards. The rifle makes a loud 'popping' sound when fired and if I were to ever purchase another one, I would get the silencer model.

As others have mentioned, good air rifles are surprisingly powerful, very low maintenance. Ammo is cheap and almost unregulated, and my brand comes 250 rounds to a metal can the size of a snuff can. The rifle is under $150.00

Incidentally, avoid the air rifles that have a big recoil pad. The 'recoil' of an air rifle is forward!