Consider going up a little on power by getting a Marlin bolt action in .22WMR. They are nice rifles with a reputation for accuracy and reliability and they are available for around $180.

WMR isn't quite as cheap as .22LR but it isn't as expensive as .223. It also gives you just enough extra power to make a real difference. Given the same throw weight a WMR will usually have slightly more velocity at 100 meters than the LR has at the muzzle. It also shoots noticeably flatter which can make for fun shooting.

WMR is favored by many hunters shooting coyotes and other moderately sized nuisance animals because the extra power gives reliable results at 100 meter ranges even without perfect shot placement. It is powerful enough to be marginal but acceptable for personal defense. In comparison a .22LR is not considered as even a marginally practical round for personal defense. You would use it that way unless it is all you have. The .22WMR gives you a lot more to work with for just few cents more a round.

The Marlin in .22WMR with a low magnification scope is a handy weapon that will fill the bill for more rolls than a .22LR. The round is not quite cheap enough to go mad with like you can with .22LR but your not going to go broke feeding your iron for casual and occasional use.