A great digression as a winter storm hits New England! Campfire fodder!
I suggest as do Alaska experts that the 30-06 Springfield is proven in Alaska but I believe it to be an absolute minimum for Bull Moose and Brown Bear. Like I hunted in Africa, I believe you should be able to shoot it off hand, handle the recoil and know how to cycle your bolt open and closed and place repeat bullets in a pie plate at say 70 to 80 yards. I did that with a .338 Win Mag and 250 grain bullets on my African Safari.
Alaska is a land of potential dangerous game! Use a rifle caliber that is in stock at the local stores in Alaska if possible. I hear .308, 30-06, 12 gauge shotgun and .22 LR are most common, but it might pay to check and take ammo precautions if your baggage is lost, like have a box ordered and waiting at the local Alaska store of your brand and special caliber.
The .308 or 6 mm/.243 Win or the new 6.5 Creedmoor I love is fine for black tail deer however if you are on an island with deer and bear, the .308 or 6mm is a “not so good” choice if a bear wants you and your downed deer. A 30-06 with 180 or 200 grain heads would perhaps be a better choice. Bigger bores and magnums are recommended if you can handle it. “Bears think that your shot is like ringing the dinner bell!”
Shot placement is everything! If you cant handle your rifle recoil then Alaska is perhaps not for you!
In Brown bear open country, a 30-06 or better a 300 Win Mag with an expanding bonded bullet is Ok. I prefer the .375 Ruger with Nosler AccuBonds or Partitions in at least 260 to 300 grain heads. I do like the .338 Win Mag as well. I shoot these very well in my Ruger M77. Further that you would be wise to have a Mauser style bolt with a claw extractor to ensure guaranteed chamber feed and removal when hunting dangerous game.
In close quarters like in tag alders where shots are less than 25 yards a pump 12 gauge shotgun with slugs. “In a brown bear charge, you must make the first shot, a brain shot count to turn out its lights.” I would not recommend that kind of close quarters hunt, but it can happen with wounded bears say some experts.
Recoil management has come a long way so use recoil pads that can absorb recoil up to 50%. Get some!
Don’t forget a sidearm like the 44 magnum with 240 grain solid semi-jacket bullets and update your Will if you are Brown Bear Hunting or fishing near Brown Bear.