A Savage .270 is a solid rifle, among my favorites in bolt guns for general use. The .270, .30-06, .308 and a few other rounds will kill anything on the N. Am continent if you do your job. Bit light on grizzly or moose, but they 'have' done the job in cases where nothing else was available, just expect to use multiple hits. Ammo won't be the cheapest, but if you have a .22 bolt action 'understudy' you can practice fairly cheaply.
My primary hunting rifle is a 7mm Mauser sporterized about 50 years ago and done very well (professional job), it's in the same performance range. You can find good deals with used rifles assuming you know what you're looking at, and for (I do), I generally don't recommend it for a first-timer.
In AR's, a 6.5mm Grendel will easily do an elk with anything close to decent shot placement, and the 6.8 SPC will do the same, when the 6.8 first got into the wild out of military hands several gunwriters whacked muley's with them without any issue (one in a Remington 700 in 6.8, the other in an AR) and I've known many guys who've used them effectively on a wide variety of medium sized game. Friend uses a suppressed 6.8mm AR for hogs in the 300-400 pound range regularly.
My primary hunting rifle is a 7mm Mauser sporterized about 50 years ago and done very well (professional job), it's in the same performance range. You can find good deals with used rifles assuming you know what you're looking at, and for (I do), I generally don't recommend it for a first-timer.
In AR's, a 6.5mm Grendel will easily do an elk with anything close to decent shot placement, and the 6.8 SPC will do the same, when the 6.8 first got into the wild out of military hands several gunwriters whacked muley's with them without any issue (one in a Remington 700 in 6.8, the other in an AR) and I've known many guys who've used them effectively on a wide variety of medium sized game. Friend uses a suppressed 6.8mm AR for hogs in the 300-400 pound range regularly.