The .22LR is a great round and with the right gun, it is a great survival option. The Kel-Tec mentioned is a good gun (I have the 223 pistol version), but under the scenario mentioned, I think 22LR is the best fit. I plan to get the 22 version of the Kel-Tec rifle as a good go-bag item.
Everyone dismisses the 22, but forgets that Hinkley took down 4 people with a 22LR snub-nose pistol. Also RFK was killed with a 22LR snub-nose. There's a lot of good ammo out there now for personal defense such as CCI Velocitors. And for hunting, when I was a kid, that's about all we used (that and a 410) and we killed just about everything we shot at (rabbits, squirrels, etc..). You can eat for a long time from the fruit of a 22LR.