Ideally, I'd have a switch barrel rifle in something like .270Win or 6.5-06 shooting 130gr or 140gr which will more than adequately cover deer/antelope/sheep, etc. over all reasonable distances; and the second barrel in .338-06 or 9.3x62 for the heavier stuff like elk, moose and bears. Standard length action, not too heavy, mild recoil, easy to buy or make brass, great bullets, proven performance, etc...

If I wasn't going to have a switch barrel rifle, then I would go with a 30-06 to shoot 180gr to 220gr (or possibly an 8x68S) if I was going to have more opportunities on the deer/antelope/elk end of the spectrum or a 9.3x62 if the majority of hunting was for game at the larger end, or if I was going to be in grizzly country most of the time even when not hunting bears.