I only three three rifle to hunt
.22 Magnum small game. pests
.22-250 coyotes and varmints
.257 Weatherby Magnum
If you say no rimfires. I would use a .22 Hornet
I use a lot of different calibers to shoot pdogs, but not counting those, I could get by with these three. If I was an elk, moose, or big bear guy I would go bigger. Maybe like a .375 H&H. At least a 30/06. My friend used to own a gun shop in Reno, he called me to tell me that he bought 4 guns from a guy's brother that lived in Montana all his life. When he died at 75, the brother sold all 4 of his guns; He said his brother lived up there all his life with no phone and no electricity.
All Winchesters all made in the 30-40's.
22 pump, can't recall if it was a 62 or the older one with a hammer.....
Model 1885 .218 Bee with a 10X Unertial
Model 70, .375 H&H with a 4X Weaver
Model 12 12 gauge 3" 30 inch full choke
Looking back on it, a guy could get by with that battery in elk/grizzly country just fine. Oh, he had a pistol too, a Colt SAA in .45, forgot about that one. All of them looked well worn, I bet there were some stories left to be told about how they got that way.