If your looking for a round for deer through elk, first off just start going through ballistics until you find what you want. A lot of choices out there. .270 is a personal favorite of mine, can't really go wrong with a 30-06, a 7MM rem mag is a great caliber, 300 is a good one, but a bit pricey to shoot and all of the 300 win mags I have shot have quite a bit of recoil to them, or you can even look at a 25-06. Great, flat shooting round, and is a good all around gun itself.
One very underated caliber in my opinion is the 7MM-08. A great round for even kids, as most models of guns that you will find, it has very little recoil on it, and is a great deer rifle that is more than capable to taking down an elk.
I would just look at ballistics, decide if you want to shoot long range, short range, whatever you want, then look at the caliber. With as many different ones out there today, it's hard to just choose one.
Or just get a 50 BMG and be done with it all!