For your uses, I'd select the .358 Winchester as first choice, next the .308, but the .30/'06, .338/'06, or.35 Whelen would do just as well, particularly if you use a 22" barrel.

(During the three years I spent in Alaska, I generally used a Mannlicher-Schoenauer carbine with a 20" barrel in .270 Winchester caliber. Although it developed less velocity that it would have with a longer barrel, it produced 2800 FPS MV with the 150-grain Nosler Partition bullet. With this rifle and load [150-grain bullet, 53.5 greains IMR 4350, F210 primers, WW cases], I killed everything the Far North has to offer, except for the great bears! The majority of these kills, including 2 300+ pound black bears, were 1-shot kills. A .280 Rem. or .30/'06 in this carbine would have been better, but I used what I had back then!)