.22 LR - squirrels, rabbits, pest control, this cartridge is just the ticket.
.30/06 - With the possible exceptions of eland and giraffe, this will do for ANY thin-skinned, non-dangerous game worldwide . . . and though I wouldn't want to use it on lion, and it wouldn't be my first choice for big bears, it's just fine for leopard.
.375 H&H - Fine for hunting anything up to and including elephant.
There might be valid reasons for swapping a 12 ga shotgun for the .22 LR, but since this is the "Rifle Country" forum, I'll let the three choices above stand.