I would go for the 350 Rem Mag(you may also want to consider the 300 SAUM, 300 WSM, and the EXCELLENT 300 WIN MAG).

Out of the 22" barreled Remington Model 673(this rifle is also available in 300 SAUM) the 350 Rem Mag should be able to take Moose and Elk out to 300 yards. If you are a really GOOD shot I am sure with PRACTICE and the right load it would be good for deer sized game out to 400 yards.

The 300 RUM is a VERY potent cartridge that ranks right up with the 300 WBY mag. As Stubblejumper stated you would need to practice shooting this rifle alot in order to be accurate with it. The heavy recoil will make it UNPLEASANT to shoot if you aren't used to shooting magnum rifles. You would have to be more specific of where you hunt, the primary game you hunt to know if it were required....No sense being over-gunned....

I am also a firm believer that in order to get the TRUE performance out of a SUPER MAG you simply MUST have a 26+ inch long barrel. I don't know what kind of terrain you hunt in but if it ever gets thick you might find yourself cursing that 26 inch barrel...