>>1604763>.223 Rem / 5.56x45For coyotes, if you own livestock that need defending. It's a great combat round against humans but not adequate for hunting anything but varmints. Included mostly because everyone should have an AR.
>12ga pump shotgunSmoothbore is the king of versatility. Slugs for feral hogs and deer at 75m maximum, buck for home defense, and birdshot for birds or maybe rabbits at a distance.
>.308 WinchesterThis is a nice hunting round, you'll find it everywhere, and you can kill pretty much anything with it except Alaskan dangerous game: griz and moose. It's used in semi-auto battle rifles as well.
>.45-70 GovernmentPic related is of the lever action variety, though stronger (and more expensive) single shot bolt actions can handle hotter loads. Typical bullets are 405 grain, roughly twice the mass of a .308 Winchester. The heavier, flat nose penetrates bone and tissue better, the cartridge can be loaded with black powder instead of smokeless, and the lower bullet velocity allows the barrel to accept homemade cast lead without fouling.
Their weakness is bullet drop after about 200-250m. Which is about as far away as you want to be shooting at an animal anyway, especially through iron sights. Think of it as a slightly lighter rifled shotgun slug that goes twice as fast.