"My only objection there was that it's highly unlikely I will ever need to shoot big game, and the 308 caliber has too much recoil for the women in my family."

It is for this reason I suggested the 7mm-08. All indications are it is mild enough even in a lightweight scout that it would be nearly as tolerable as a 243, shoot nearly as flat, but have superior terminal ballistics and better in the brush. Although Col Cooper never addressed the alternative to the 308, most from his program suggest it is quite capable.

The 22 lr is a good cartridge for practice and for taking small game, but faces too many limitations to consider it as effective as high power centerfire rounds. This is not to say it is useless, just too specialized. Someone proficient and sensible will be able to make the most of having a 22 for survival. It depends, too, on what you are trying to survive. For my consderations, a centerfire high power lightweight bolt action rifle makes the most sense. I wouldn't turn a 22 down if that's all there was, just not my first choice.
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The ultimate result of shielding men from the effects of folly is to fill the world with fools.
-- Herbert Spencer, English Philosopher (1820-1903)