I’d take a good lever gun personally. If you could find a used Marlin or Henry in something like 30-30, you would have enough power to deal with most anything you need to shoot. One of the carbines in 44 Rem Mag or 357 would also work well closer up, and give you a few more rounds. Check family owned gun shops or pawn shops in your area. Unless you plan on hunting longer ranges, you wouldn’t need to put on a scope. Skinner has nice large aperture peep sights you can put on the back. They’re fast and easy to sight with, and durable so you don’t need to worry if the rifle gets knocked around while hiking.