Of the three cartridges listed, my choice would be the .300 win mag. It has the range of bullet weights, velocity and power for just about any North American animal. It is also popular enough that should you need it, just about any Podunk store carries ammo for it.
I killed most of my elk with a .30 Gibbs, which is an improved .30-06 that is close to .300 Win ballistics.
The 7 mm Rem mag is a fine deer and elk cartridge, and I've easily killed elk with mine, but mine has been reduced to my back up foul weather rifle. My favorite rifle now for elk and for international hunts is my .300 Weatherby (a .300 Win on steroids).