I have to agree with an earlier comment, that for anything in the lower 48 states, the 30.06 would be enough gun, provided the larger bullets would be used for elk, moose, grizzly bear, and bison. And for those animals it still might be marginal.
Alaska is another story. I was stationed in Alaska twice, and the state fish and game recommended a pump shot gun with slugs , and the Marlin 45-70. The reason being those animals are very large, hard to kill, and the normal ranges are very short.
As the 35 Whelen is pretty much the equal to the old 350 Remington mag, it would also work on most game, but I would want the most powerful thing I could reasonalbly carry, those moose, grizzly bears, brown bears, and polar bears are very large, and with the exception of the Moose, very agressive. The truth is moose kills more people up there than the bears, and when those animals charge they are very close, and for me the lever works faster than a bolt. So as for me and mine, we would carry an older Marlin, or a new Henry, or even one of the 1886, all in 45-70. Have to understand as a non resident of Alaska, a professional guide is required for any bear hunt, or sheep hunt. Makes hunting in Alaska expensive