I have been reading Jack O'Connor's 1978 edition of
The Hunter's Shooting Guide, originally published in 1957. When posed with the question of "The All-Around Battery", his answer was
With a .22 rimfire for small game and birds, a .30/06 for everything else from Impala to elephant (with 220-grain solid bullets), and a 12-gauge the owner of the three gun all-around battery could do very well in Africa--or anywhere else!
I guess Jack didn't count handguns, even though there is a section devoted to them, but he did count shotguns.
