If I was in your shoes, I'd pick the 30-06 first hands down. It shoots flat enough for shots out to 300 yards or better (if you take the time to pracitice) and has plenty of power for bears, elk,etc. You can find ammo anywhere and it isn't usually finicky about what you feed it.
I have 30-06, 280, and 243 and don't feel handicapped with any of them on deer. I handload though which makes the 280 a good option since factory 280 ammo isn't widely available here.
For close seconds, I'd chose the 308, 270, and 7MM Mag in that order. A 308 is about 90%+ that a 30-06 is(some will argue the point but they're really close). The 270 is definately not a bad choice for deer, and it has been used on elk and bear successfully. The 7MM Mag is last on my list because of the additional recoil, noise, and barrel length associated with this round. I'm not knocking it by any means, but if you're new to high powered rifles, it may not be the best first one. All three offer alot of options for bullet weight or construction and can be found many places in factory ammo loads. Good luck.