I will agree with 79S on the 338. I have "The Ugly Gun" a Ruger M77 stainless synthetic in 338 and have taken it to Alaska and Africa twice each. A tough and durable rifle in a great caliber.
If you want a Winchester 375 H&H get the best a pre64 M70. Second choice (if you can call it that) A Ruger in 375 Ruger.
Bingo, excellent post GSP buddy...