Well, in short... I would go with a solid bolt action. That means a savage, or better yet, a remington 700. I love my lever actions, but they are more of brush guns rather than long range nail drivers. The as far as caliber, I would say .270 is the smallest I would use on elk, and even then thats iffy. Go with a solid cartridge in the .30 line instead. .308 or .30-06 or both wonderful. Between the 2 would be personal preference. .308 is a bit more accurate, and if this is going to be a mostly range gun, then you wont have any problem with shots up to 600+ yards. Cheap(ish) surplus ammo can be found sometimes also. If this is going to be a primary hunting gun, then a .30-06 is the way to go, the reason being there is a whole range of different weights and loading so you can take everything from deer to bear.
Bigger rounds like .300 win mag, 7mm rem mag and higher are also great choices, but they are a bit more expensive to shoot, and take a harder toll on your shoulder. The benefit of these rounds is that they hit much harder at longer distances, so if you feel the only shots yours going to be able to take are going to be in the 400+yard range, then maybe this is the way to go,