I can see a few possibilities here, and all branching on scenario.
First of all - RULE OUT TEOTWAWKI. The second society breaks down, we'll have the military and martial law hauled on faster than you can get your AR's loaded. Besides, we're America. If the military doesn't step in, then every mall-ninja, gunshop-commando, paranoiac, and ghetto-soldier will be locked, loaded, and unloading on anything that moves anyways, such as each other. Have fun, I'll be in my basement with a beer, milady, and whatever shoot-em-up movies I can find.
So, we're left with an event putting you into the wilderness, outside of cell-range, and needing to survive. If you REALLY want to talk ANYWHERE, it's the .22LR. "Survival Rifles" all seem to use it, and they have no doubt had a LOT of time put into their development by people discussing things like this. It's light, easily-carried, not-loud to disturb other animals, and still powerful enough to take down what you'll NEED.
What you NEED, btw, are animals not much larger than Coyotes. I know, it sounds nuts, but really, having excess meat laying around your campsite from a deer or caribou is an opening for pathogens and worse - other predators your little .22LR won't really take good care of.
If you're going to be going off-the-grid to a cabin, and are leaving modern society, then pack a reload kit, save up ALOT of .264, and run a bolt-action 6.5x55SE. It's got low recoil, FLAT shooting (better guarantee of a hit, thus better use of ammo), and will take down anything from coyote to caribou. I went with Low recoil so that if you injure a shoulder or pull your back (VERY high chance injuries living in the open like that), it can still be fired. Also a point with the .22LR.
In terms of Varmints/squirrels/small stuff with a 6.5 - Well, if you're established, you should have containment for food, and thus, why are you worried about little stuff? The varmints shouldn't have rounds wasted on them, they should have traps set out. They're curious, but dim.