Playing the - I am going to be in the wilds for a number of years and need to feed myself game:
22lr - very versitile and ammo is lightweight, and compact. I would have a Brno or CZ 452 bolt action fitted with open sights, plus a slim 6x42 or better a 6x36 scope. And a case of 22lr HV ammo (not tye ultra high stinger), with a mix of mostly hollow points but a good number of solids. Why HV - well it has that extra bit of power and penetration that allows it to shoot much bigger things than it was intended for.
However, I could make very strong arguments for a 22 magnum rimfire or the 22 hornet. A bit more capable on deer sized animals, but ammo is still very compact and light.
With 22rf you can 500 rounds into the space a box of 12 bore, Hornet - more like 300. But either way they keep you going for a long time. 223 size is getting a bit powerful for small game and birds if you want to eat, but does add good range on the rifle.
If I was going to have a centre fire rifle it would a lighter weight sporter, again with open sights plus a small slim scope. Calibre doesn’t matter per se - anything from 6.5 up to 30cal / 8mm will do. Bullet choice is far more important and you want something that both expands and has good penetration. And 100 rounds or even just 50 would keep you going for a long time. 308 win would probably be the sensible choice as ammo is everywhere.
But i would probably ditch the centrefire and carry a shotgun instead as much more versitile, and gives the opportunity for shooting flying ducks, geese etc, and with slugs its pretty good for deer and protection sub 70 yards. Ammo is the challenge as its heavy and bulky. Type - well a good side by side is handy and versatile and robust. Lots of arguments can be made for a pump action or semi - but they do contain a number of little springs that are prone to rust a breakage. Whereas a good boxlock is simple and go on for ever. 12 is the obvious choice of calibre.