If I was only going to only hunt elk I would get a 338 win. And If my budget was endless my recommendations maybe a little different but......
All That being said, I put together a pair of rifles for out west (all species) a couple years ago and went with the tikka (light or super) in .300 win. The guns have a good price, light, best factory trigger available once adjusted(my .02), and they shoot anything you cram in the chamber exceptionally well. I picked the .300 win over the WSM because of ammo availability and variety. You can find about any combination of brand and bullet you want and in a pinch you can find something just about anywhere. I am a long time fan of the .300 wsm and if you choose that caliber you can knock about 2 inches off of the barrel length.
Topped these with leupold glass with the CDS system. I wouldn't recommend anything less than a 14 power. I prefer a 30mm tube (more light and more adjustment) and a 50 mm objective. You can stay with a 1 inch and 40 mm and shave some weight. Don't skimp on rings. There's a lot of good choices like Talley (probably the lightest), leupold, or the vortex precision matched (my choice)
Feed either of these 30 calibers a good Nosler bullet from 180 + and you can give a big elk a dirt nap at a pretty far distance