I have read multiple articles stating that 1500 ft lbs is a good minimum for elk. That being said, I think any caliber from about .25 on up is a good diameter for elk sized rounds. That being said there a lot of things to consider.
The terrain you will be hunting. I have seen hunts take place in close in heavy timber, in this kind of area long range ballistics aren't really necessary. However if you hunting out in the mountain ranges where it might be 400 yards to the other side of the valley, you might want a faster magnum cartridge so that it still packs that energy and trajectory way out there. However I think long range trajectories aren't quite as necessary these days with the fancy rangefinders we have to eliminate range estimation errors.
The shot you take can be important too. If you intend to try to smash through the shoulders to put the elk down right there, you will want more of a powerhouse caliber with a heavy for caliber premium constructed bullet. This is also important if you want to take a steep quartering shot. However if you intend to take what I call an archery shot, aiming to put a round through both lungs and hopefully the heart, this is where you can use the lighter calibers with success.
Any way you go, I do recommend a premium type bullet because the elk is a large bodied animal.
If I had to recommend a decent all around choice, I would choose the good old 30-06 with a 180 grain bullet like a Barnes Triple Shock X bullet, Nosler Partition, Swift A Frame, or maybe one of these newer all copper bullets like Nosler E Tip or Hornady GMX (though I haven't shot any of these newer type all copper bullets).
If I was hunting at extended ranges, I would up it to a 7mm or .300 magnum with some type of tipped premium bullet to help with the longer range energy conservation. Something like a tipped Triple Shock X Bullet or Trophy Bonded Tipped bullet. I haven't used any of the Winchester XP3 bullets either but they would probably be a good choice. I hear people have problems with them due to their coating though, you need to shoot several rounds to get that Lubalox coating in your barrel before they start shooting good, well that is what I do if I am shooting moly coats anyways.