3 thoughts. And a huge long disertation on calibers.
I lived in Barrow, Sitka, Anchorage and Fairbanks. I have killed exactly zero bears.
I would not hunt brown bears without a back up hunter with a 7mm. Get the biggest rifle you can shoot well.
The 416 Remington, 416 Ruger, 458 Winchester and so on probably have too much recoil for you to want to practice and will be heavier.
If you are going to be by yourself or with a buddy. A big rifle 375 H&H/375 Ruger whatever is a good option. Another great option is the 9.3x62/9.3x64 rounds from Europe. There are Sako, Tikka, CZ, Rugers and other rifles available in that caliber and ammunition is available in Anchorage. Probably at Sportsmans in Wasilla as well. The other classic Alaska bear smasher is the 358 Norma.
The 9.3x62 shoots a 250-300 grain bullet about 100 FPS slower than the 375 Ruger/375 H&H do. Terminal performance is very similar. The 9.3x62 is based on the 30-06 so you get 5 in the magazine. Hornady, Remington, Winchester, RWS, Norma, Lapua there is a ton of ammo for it.
The 9.3x64 is a rare cat, but I have seen them for sale in Alaska. I think they were old Sauer or Steyr rifles. The 9.3x64 ammo is also harder to find. Only RWS and Brenneke make ammo for the 9.3x64.
Only Norma makes 358 Norma ammo. Factory rifles would be of Scandanavian manufacture. Schultz Larsen, Sako, Husqvarna. Not super common at all. Classical Yukon and Alaska bear smasher.
Alaskan Eskimos hunt Polar Bears with a 223.