I'm partial to the .30-06 due to its usefulness across the entire country, the wide load selection, and the great killing power. On the other hand, you can cut your rifle's weight a bit by going with the .308 (shorter action). The .308 has a little less velocity and energy than the .30-06, but not a whole lot. The .300 Magnums are great for longer-range shooting, but frankly I don't find them necessary in most hunting situations. And yes, there's that recoil to contend with.

All are capable big game calibers, so I recommend reading up, shopping around, and talking with some more hunters. Good luck!