I personally haven't hunted Elk at all. But considering for my area (Canada) you can hunt the deer with anything smaller then a .243, I would suggest a .270 or a .308.
Now If I was to be buying a new rifle, it would most likely be in .308 for a couple reasons. One being that if I was to get into hunting, it would be a heavy enough caliber to take out any animal on this continent. The second reason would be that if I wasn't a reloader, I could buy bulk ammunition at a fairly reasonable price during the off season for range use.