Keep in mind that there is a difference between "caliber" and "cartridges." Many people incorrectly and improperly use them interchangeably. Caliber refers to how wide a bullet is. A .308 caliber bullet is wider than a .284 caliber bullet. A .30-06 and .300 Win Mag both use the same caliber bullet - .308, but the .30-06 and the .300 Win Mag are different cartridges.
That said, the .30-06, 7mm Rem Mag, and the .300 Win Mag are all fine choices for game up to elk. The .300 is the better choice for elk at longer ranges, but the .30-06 will work just fine on elk within 200 to 300 yards or so. The .300 just shoots the same bullet faster, that's about it.
The 7mm Rem Mag is one of my favorite cartridges. However, on big game such as Elk, I think that the .300 (with its .308 caliber bullet) is a better choice.
Forget about what the numbers tell you. Go out and shoot each gun if you can, and determine what recoil level you can handle. If the .30-06 is the most you can handle (and that is, if you can really notice the different in recoil), then get the .30-06. No gun in the world is any good if you can't shoot it accurately because of flinching from the recoil.
Whatever you do, just make sure that you use premium bullets. In the .30-06 use 180 grainers, and no less than 165 grainers. In the .300 don't use any bullets lighter than 165 and, if on elk, use at least 180 and go up to 200 grains. In the 7mm Rem Mag, use no lighter than 160, and go up to 175 on elk. Premium choices are Nosler Partitions, barnes X (TSX), Trophy Bonded, etc.
Zachary