"What's the best gun" is something like" what's the best food" or "what's the best tool."
For an accurate, inexpensive rifle with enough power to kill predator-sized game cleanly, and with little noise and no recoil, I'd recommend a .17 HMR. It has the same powder capacity as a .22 magnum, but will push a bullet at 2550 feet per second. The light (17 grain) bullets are frangible so there is very little ricochet risk and they don't over penetrate. The Savage model 93, with a 2 or 4 power scope would be ideal.