Yes. Modern Savage rifles are very accurate and that 300 is as good as any for killing them. I have seen a Moose killed with a 308 so a 300 Win Mag will do fine.
I'd go for the 111 FXP3 in 300 Win Mag or the 11 FXP3 in 300WSM, they are the same weight and price and either will do the job. Some people might prefer the 338, but there's not really a significant difference. 30-30s have killed a great many elk, so a 300 magnum of any sort won't have any problems.
At 200 yards, which is as far as I'd dream of shooting off-hand, a 300WSM or Win Mag deliver an almost identical 2578 or 2598 ft.lbs, the 338 Win Mag that some would push you to will push that to 2815. Less than 10% more, but at the expense of having more bullet drop and recoil.
At longer ranges the flatter shooting 300s are going to give you an better chance of nailing your target than the perceived extra energy of a bigger round.
I've always had a thing for the 375H&H but despite kicking the hell out of the shooter and having a lot more muzzle energy it delivers less at 200 yards than the 300 magnums.
PS. Take the energy numbers with a grain of salt, there's so much variation in ammo, but they are OK for comparison. That's a couple of 180 grain 300s and a 225 grain 339, all spire points.
PPS. If I were buying now I would look very hard at the 111FCNS and 111 Long Range Hunter, the AccuStock looks like a very good idea.