Used a 35 W IMP Remington 700 for many years. It was a 30-06 that was rebored by LaBounty in the late 70's and fitted with a Brown Precision stock. If you don't reload it's a caliber that gets eliminated but there are several other things that I would consider.
300's, 338, 375 all are generally heavier than non-magnum based rifles. I don't like to carry more than I have to.
Synthetic stocks, to me at least, are the thing for Alaska. In 1974 I used a walnut stocked 35W IMP on a Springfield action. 22LPI checkering, beautiful wood. After about two weeks hunting, living in a tent, rain, cold I decided that synthetic was the way to go. Wood stocks take a beating in that kind of weather.
Ended up with two Remington 700's in Brown Precision stocks, 30-06 and the 35W IMP.
Enjoy yourself.
Stainless is a good idea too, although I always carefully waxed everything, reassembled, checked zero and never had a problem with rust (except for volcanic dust).