If you want factory ammo then the 300 Win Mag is the ticket. You can get premium loads that will do anything you want to do. You can go very heavy bullets or very light, your choice depending on what shooting at.
Go with either the savage or rem sendaro. Have a muzzle brake put on and have gunsmith make a knurled end cap that will cover the threads so you can take it off. That way you can practice more and take less recoil until you become used to it and then take it off to hunt (after reconfirming zero).
Have gunsmith skim bed it, check crown, and lap the lugs and do a 2.5 lb trigger job also. Should shoot 3/4 MOA with decent factory loads.
spiritwolf68 - their are a lot of people here with great knowledge of the shooting sports ,a lot of people who specialize and compete in games that contribute to the skills they need in their hobbies , people who spend the time and money learning and practicing their skills . please don't get hung up on the Magnum issue , most people don't shoot them well ,the general public who hunt , practice very little , my outlook is to shoot the biggest gun that your SKILL allows , the caliber you shoot the BEST and are the most COMFORTABLE with - my friends and I have a game we play, starting mid summer before hunting season, we mark off 200 yards -( to the targets and back) we have 15 pound packs(two - 1gal milk jugs filled with water) and our rifles ,we run that 200yds ,1 minute to set up and load , get our breath and 3 minutes to shoot 15 shots - 5 standing ,5 kneeling and 5 sitting . It doesn't sound very bad - but try it and see what scores you get . it's only 100 yards , oh , looser buys burgers and a beer. ya gots to have a bet - ha ha ha - good luck
I agree with old fart (who's name I love btw), however you mentioned 3 BIG beasts. 300 WSM would be fine. The Barnes 168 Triple Shock would only produce 20-21 lbs of recoil (with a 10lb . So you wouldn't need a brake. I wouldn't shoot a buffalo at 500 yards or even a moose, maybe an elk. But inside 250-300 you should be ok.
Note that I'm not saying that combo won't kill at 500 yards, But those animals are expensive to hunt and I want to recover them cleanly. You also mentioned your not a great shot.
Well I have narrowed it down to 2 rifles the .340 weatherby sf and the remington modle 700 sendero sf .338 ultra mag ,but the ballistic seem like the weatherby is a flatter and farther shooting rifle. on a 250 grain sp bullet it shows the weatherby 100yards 3.9, 200=4.6,300=0.0,400=-11.1,500=-29.6.
And on the remington the same bullet 100=1.7,200=0.0,300=-7.6,400=-22.1,500=-44.9.