I really only use my 12ga for waterfowl.
You can hunt anything on the continent with a 45-70 if you do your part as a shooter and learn well the trajectory. You can load #6 shot in a 45-90 cartridge, neck it down a touch so it fits the throat and hunt upland game birds and small game effectively using a 45-70 rifle. 243 is also a very versatile cartridge - an excellent choice for a hunter looking for one rifle to do everything. That said, old timers hunted brown bear with the 30-30, but I think balls were bigger back then.
First though, every hunter should own a .22 long rifle.
Lots of hunters these days are concerned with what rifle is appropriate for what game but in reality, I think a rifle you shoot well (fits well, comes up to your eye comfortably) is what's important. You should learn how to find the vitals of anything you hunt, learn the terrain and know where your firearm's POI is at any range you expect to hunt at. Action choice is not very imporant. You really only should need one shot. If you don't believe me, spend some more time at the range ;-) I never had anything except a single shot rifle until I turned 26 and it never hindered me in the slightest. A single shot rifle will teach you to wait for the shot.
If your hunting for pelts, than a 22-250 or .243 is a very good choice. The wide variety of commercially available ammunition makes either good for anything from rabbits up to deer as far as not destroying your hides.