.22 rimfire (cheap and for the pot)
6.5X54 or 55 (flat shooting and light)
8X57 ( good range of medium to heavy bullets; deer to large thin skin game)
.375 H&H (no question about all around) or .404 Jeffrey (the .404 only because it is what it is!)
20 gauge sxs cyl / cyl

Always a good question.