'Playa. You didn't say what game you would be going after but here's a few sense worth. I've taken deer and elk with the venerable .30-06 using the 150 and 180 grain bullets respectively. This caliber is the most popular in our elk camp which averages 14-16 shooters each year. You can make an .06 shoot like a magnum (greater energy at extended ranges) by using the 165 grain bullet as opposed to a heavier one and using the "point blank" technique for sighting in. This will put you withing a deer or elk's vital region from the muzzle out to your 300 yard stated limit. There was a good article on this in Outdoor Life about three years ago. Rick Jameason in the Shooting Times had an article early last year (believe it was Jan. 01) on the point blank method. You can go to galleryofguns.com and do a search for his article.
Having said all this, I got a Rem .300 RUM last year. My .06 was fine but got too lustful. It's a bruiser in terms of raw power. I'm hoping to get an elk in the recticle this year.
What I discoverd in comparing my .06 and the RUM was that the 26 in. barrel and added muzzle break on the RUM give it a very different feel from my 24 inch barreled .06 BAR. I end up doing a lot of practicing at snapping the RUM into an offhand position to get used to it's longer barrel and different balance.
In addition to the .06 and my RUM, shooters in our camp also use the .308, 7 mm Rem Mag and the Win .338 Mag. All work fine and all have taken elk.
You really can't go wrong with any of the guns mentioned in the posts above. Good luck