For any sort of 'survival' or bug- out scenario I can envision, the rifle I would personally reach for is my SKS.
I also have a Ruger 10/22, but the .22 is simply not enough gun for deer or bad guys, in my eye. And I swear, we have more deer than squirrels here in southern Illinois. Why would I want to spend all day every day popping enough rabbits, squirrel, and birds to keep me fed, when I could just as easily shoot one deer and feast for several days?
I do not suggest that the SKS is the best all around gun for this, (I wish it were more accurate) but I would choose it over my bolt action and .22s because it's the gun I'm most familiar with. Of the thousands of rounds I've put thru it, only a handful have been at paper. I carried with me every day out in the fields, and used it on everything that walks, crawls, flies, slithers, or swims, from grasshoppers to coyotes. (I haven't actually taken a deer with it since that's illegal here, but have spoken with people who have.) It has taken coyotes at over 200 yards, and with the bayonet.

No dirt clod within 300 yards is safe, and if I have the luxury of several shots, that distance can be increased to 500-600 yards. (semi- auto comes in handy there too.) And yes, this round will still kill a rabbit or squirrel just as dead as a .22. Ammo is cheap enough to stock up now, and more importantly, practice a lot.
Aside from the caliber difference, I'm surprised so many of you have chosen to depend on single shots. I haven't hunted with one for years. Hey, those quick follow up shots come in mighty handy! Time and again, the repeater has made the difference between one critter for the pot, vs. three or more. Sometimes, when I missed a critter with the first shot, (I know it shouldn't happen, but it does. To the best of us.) it has enabled me to take it with the second. I mean, since we're talking about a survival scenario, it could mean the difference between starvation and a full belly. Even in the realm of .22s, there are several take down repeaters on the market that could stow easily enough to keep nearby all the time.