Best .22 air gun for hunting small/medium game?

I'm seeing squirrels, ground hogs, rabbits, raccoons, and other pesky vermin getting my dads garden. I need a gun under 300$ that will cleanly kill these animals. What in your opinion would be the most accurate and powerful gun for killing these animals and best pellets. I'm looking at the walther falcon hunter .22. Any suggestions. Best answer 10 pts. Thanks