I have a Remington .338 Win Mag, and used it to take my 8'3" Russian brown bear. One good hit, and the bear went straight down. Ditto for a hunting partner who also used a .338 on his brown bear.
It's strictly a business rifle if you shoot full power loads. I'm only good for twelve shots off the bench with these loads. Then I close up shop so I don't develop a flinch. The .338 isn't gentle, but it sure did the job on those big bears!
There are milder handloads listed, but I haven't tried them. I've used a .30-06 for most of my other U.S. hunting.
If you plan to hunt dangerous game in Africa, the .375 is a better choice. If you are only hunting North America, the .338 is a great choice.
I suggest you try working the bolt (uncocked) on whatever rifle you get. With a Remington rifle, I can slap the bolt open and closed with the palm of my hand in about the time it takes to work a lever action. This doesn't work as well on some of the other brands of rifles that I like.