If you're gonna be hunting the BIG big game, you're gonna want a high-quality bullet that will not fail. Some of my personal favorites that will serve you well - Speer Trophy Bonded Bear Claw, Winchester Fail Safe, Barnes Triple Shock, Nosler Partition, and Sierra Game King. The 150gr would probably do the job, but you might consider moving up to the 160-175gr bullets for the really big game. That's a great gun, and it should serve you well for a long time. I'd love to get a model 700 one day - my dream rifle is a 700 LTR, probably in .308, but I'd be happy with a 700 classic in a more unique caliber, like .264 mag

Good luck!