I use two rifles for elk hunting. I know it's rude to answer a question with a question but the question back is what kind of hunting are you going to do? Are you going to hike in or will you be on horse back or in a truck mountain road hunting.
Let's assume it's horse back. A bolt action is standard but you will want to keep to a 40mm objective on your scope as most rifle scabbards are not designed for the 50MM scopes. Even the new Leupold that bends over the barrel gets stuck in the scabbard. Still leaves you lots of options. Same problem if you plan to have a bipod attached to the stock. You may want to get a set of your own saddlebags and make sure you bipod will fit. I do not use one. As the horse will be hauling your rifle up and down the hills all you will have to do is be able to carry it a few hundred yards to a stand or to put the sneak on them. The same will follow for truck hunting. both of my guns are in the 9 pound range. Not too heavy to slow me down and heavy enough not to kick the snot out of me.
If you are going to back pack hunt then weight is a premium. The down side to light weight is it will kick the living snot out of you. You may want to go with a 30-06 or one of the other non mag 7's like .284 or .280 or even one of the .25's either 25-06 or 25 win super short mag. (WSSM) and limit your shots to 300 yards.
As I said I have two elk rifles. The first is a Win M70 classic super grade in .338 Win Mag with a Weaver Grand slam 4.5-14X40 scope. Do you know scope power? Lets say you don't, the 4.5 is the lowest power it will increase to 14 power and had a 40mm objective ( the big bell pointed to the game diameter).
The second is a Sako AIII in 375H&H with a Leupold fixed 4 power scope.
I bought both of my rifles used at good prices.
Both rifles are sighted in for 200 yards and I am confident to 250 with the .375 and 350 yards with the .338. The 375 was purchased as a brush elk rifle as well as a back up.
I like heavy bullets for game. Of my friends, one uses 7mm Mag, one uses 7mm Shooting times Western (STW), two .338 Win Mag, one 30-06, one 300 Win mag, two 8mm Remington Mag, and another uses .257 Weatherby Mag. But all of us have almost identical scopes. A good compromise would be a good 3-9X40 Weaver or Leupold.
Had I to do it all over again. I think I still would go with .338 but I would look at one of the stainless / synthetic stocked bolt guns. Rifles get beat up in the back of trucks and on horse back. Horses love to walk under trees and the branches bang off of you and your gear. Do not forget a good clear pair of binoculars about 10X42.
Any standard bolt action rifle will work. You can even go for a single shot, like a Ruger #1.
I agree with Peter Capstick ,Famous African hunting guide and writer, and shoot the largest caliber you can shoot well. You should find a budget for your rifle, scope, sling, soft case, and at least 100 rounds of ammo. I use the Remington core lok 225 grain soft points in the .338 and the same bullet in 270 grains for the .375. They are accurate, cheap, and easy to find at some local shops. With large belted rounds the standard bullets work fine on game and premium bullets are not needed. Shot placement is paramount. Shot placement comes with practice. Shoot often. Maybe only a few rounds each session but shoot it every time you go to the range. Try and find a local club that does a running deer shoot. It will help your shooting a lot.
I like wide 1 1/4 inch slings. When hauling out game it keeps the rifle on my shoulder better the the 1". Other than that I walk a lot before the trip with a step aerobic stick in either 9 or 15 pounds and a small back pack with 20 to 30 pounds of junk and get used to carrying the rifle and hauling weight. Better to get a rifle you enjoy shooting and like and get in shape for your hunt than buy a super light rifle you hate shooting. If you don't like it you won't shoot it and you won't hit what your elk when the time comes!
I also said a soft case. If your hunting out of a truck or moving horses around the soft case will keep your rifle from getting dinged not to mention in camp. the seat material of the back seat of a Ford pick up will rub the blueing off of your gun bouncing down dirt roads. You may fly to your hunt with a hard case, but pack a soft case as well.
Once you get into elk country the standard belted mags are available in most sporting goods stores as well as some grocery stores and wall mart in case you forget or looses your ammo.
Truth is until the 1950's your standard deer cartridges were also elk rounds. With premium bullets and a lot of practice your deer rifle would work as an elk rifle. Two years ago my friends brother in law shot a nice 6X6 with a Winchester 94 carbine in 30-30. One shot right to the heart. Dead Elk 120 yards form the truck.
