I assume you mean a 300 win mag which would fine for what you mentioned. But you did mention griz bear so I would look at adding a 338 win to the top of the list. Assuming you have either a capable or other means for the smaller game such as deer the 338 would give you a nice cabinet with some extra thump for the moose/elk hunts (not to mention the critters that bite back!!!).

Ultra mags or wby mags would be other choices you could consider, not required but food for thought.