ORIGINAL: Redclub
Do you seriously consider that you will go to Alaska, If you can afford $10,000 or more for a bear hunt than a special rifle should be considered. Either a 308 or 30-06 are fine rifles and get the one you choose but do it for what you are going to hunt most. Remember it can take different optic's for dangerous game.
Redclub
With a little luck, I may end up living there one day. That's the only way I will be able to afford a brown bear hunt. $10,000 is only the low end for a guide. They can go twice that amount or more, plus you have to buy a $500 tag, airfair, etc... I wish I had a close relative up there. That would be another way to afford it.