Thats kind of a broad range of game u intend to hunt with one gun. For Coyote/Deer and even prairie dawgs, definetly a 243 winchester, . You can get bullet weights from 55 to 100 (i think 105 if u handload). But for small game that would be to much gun if u plan on eating them. I dont personaly think any .22 weather rimfire or centerfire should be used on deer, many others feel the same. For game smaller than coyotes the 17 hmr is hard to beat. Some do take coyotes with theres i just dont feel theres enough power for that large of game. 17 for small game. 243 for coyotes and deer. If u do decide to get a 22 cal at least look at the 223 remington, CHEAP to shoot, TONS of loads.