Am glad 'pezhead' mentioned the T/C Contender... 'cuz other than the single shot restriction you can address the limitations of only one caliber easily. 2 or more barrels.
But you can also get switch barrel versions of of guns and spend similar amounts or maybe less money.
Interjecting final cost, weight and pack bulk into the choices mix brings in more challenges to the decision.
Clearly, there are many options and one or more compromises will be needed.
Sticking with .22LR as one caliber choice makes obvious sense as you can carry more of it and its a good multi-task choice.
If pack-ability were important and 2 guns was an option, I'd like a folding stocked Ruger 10/22 and Winchester Model 12 in 20 or 12 gauge, The model 12 takes down so it's easily stuffed in a pack, though probably only with the 20 inch or less barrel...which is my choice. Defense with a pump shotgun is met, as is versatility in ammo. And both guns can be used for hunting.
Good luck shopping.