Reily:

For a first big game rifle, it is hard to go wrong with a bolt action chambered in .30-06. What is nice about this selection is that if you add more specialized rifles later -- a .25-06 for pronghorn antelope hunting, a .338 Winchester Magnum for elk/moose hunting -- you can still take the .30-06 along on these hunts as a back-up in case the preferred rifle becomes disabled for some reason (when you drive 1000 miles to hunt out of state having paid several hundred dollars for a non-resident tag, it is better to NOT have your hunt scuttled because you only have one gun and it fell out of the truck in the dark unloading things at the hotel when you arrived exhausted after your long drive -- didn't happen to me, just an illustrative scenario -- it is a very good idea to bring along a back-up gun).

If you have no rifle shooting experience, I would have some reservations about having you start out with the .30-06 or other powerful centerfire rifle. I'm not saying it can't be done, but it seems there are better approaches. For example, a lot of people get to powerful centerfire rifles by way of first shooting BB guns, second shooting .22 LR rifles, and then the centerfire rifle (maybe with some shotgun shooting experience with 12 gauge 2 3/4" shells also). If you are totally new to rifle shooting, it may be beneficial to get some experience with a BB gun to learn the fundamental rifle shooting positions (standing, kneeling, sitting, prone). You can even improve your most basic marksmanship shooting a BB gun at targets at 5 yards range. The sweet part about this recommendation is that you can pick up a Daisy "Buck" BB gun for about $18 and you can practice inside. This may seem a humiliating practice for someone chomping at the bit to be pulling the trigger on the .30-06, but if you are a rank beginner it will pay dividends. I would guess that a large number of rifleman have extensive BB gun experience in their past, before shooting their powerful centerfire rifles. I'm getting my youngest daughter started right now shooting just such a Daisy "Buck" BB gun, and I can tell you that it is a challenge for her to shoot well and that -- thankfully! -- I shoot better than she does (the point here is that up to a certain level, marksmanship can be trained and improved with such a simple, cheap tool). Something to think about. I mention this because you did not indicate any prior experience.