For hunting, 338 RUM. For extreme range plinking, you can add the 338 Edge/Mystic/Tomahawk and other variants of the 338-300RUM to the mix but the difference is not huge and you will need a 4" mag box.
Rem is your action of choice. Dirt cheap and more then accurate with a bit of tuning.
However, the recoil on these two are BRUTAL. You will need a muzzle brake and that is no fun to hunt with unless you plan on stand/static hunting.
Unless your ambitions including dropping big animals beyond 800yds, there are so many better more effecient choices.
A 338WM is way big enough for any NA game a very long ways from the muzzle. The 300WM and 7RM are also more then enough as thousands of hunters have proven.
Then there is the 30-06/270/308, etc, etc, etc.
Jerry