>>2641207It depends on what you need it for. As other anons have already suggested, something in .22lr is a good choice for a first gun. Recoil is practically non-existent, ammo is very cheap and ubiquitous. You can take squirrels, rabbits, birds, maybe a marten with it. They are also great for plinking cans and whatnot.
.223 is a significant step up in terms of energy and would be my suggestion. Recoil is still very light and ammo relatively inexpensive, except now you can confidently take foxes, badgers, coyotes, racoons, all the way up to deer-sized game with it; at a distance, as well. I'd try to keep it within 300 meters for hunting though. For target shooting, it will also serve you exceptionally well beyond that.
If you need something for defense against bears and other wildlife, but something that can still be carried on an everyday basis and great fun to shoot at the range, I highly recommend a .357 Magnum, preferably in a 3-6" revolver configuration.
If you want a proper, high-powered hunting rifle for taking big game like wapiti, caribou, brown bear, moose, I would find it uncouth to suggest anything other than the .303 given the beauty and history of that cartridge and the nature of this thread.