Maybe it would help if this steered more toward survival, can't rely on finding other ammo sources, so you naturally pack only 2 calibers.
Please try to keep the answers to the question, which one gets 22lr and which gets other caliber.
Even if you've got a fancy gun that accepts multiple calibers, there is probably going to be only one caliber you would grab over the others.
This is for stuff you would have to carry, and shotguns were not a part of the question. Besides, anything you could hunt with a shotgun, you could take with a large cal handgun or rifle, but not vice versa. Shotguns and ammo are heavier and bulkier, so they're ruled out.
Keep the answers coming, and maybe with a rationale as to which way you go. =)
Good luck hitting a bird in flight with a pistol or rifle.
There is a reason people, say shotgun. The only things they cant do is conceal very well like a pistol or shoot long range like a high powered rifle, however with modern slugs they can reach out to 150-175 yards.
You can hunt birds, large game, short range self defense with buckshot, extended ranges with slugs, and there sre specialty rounds for door breaching, busting through barriers, less lethal rubber bullets, beanbags, homemade rock salt rounds, etc.
However if shotgun is ruled out and we aren't allowed any multical guns, which is highly impractical, always take the best equipment available. I say a 10/22 rifle and a hicap .45acp, likely a double stack 1911 of some sort for me.