RE: 30.06, .270 or 7mm
Well any of the 3 you mentioned are good for anything in North America for all but maybe the great bears and Alaskan moose, but I'm sure each of the 3 have taken more than thier share of both bear & moose.
The 270 will be the lightest of the three in recoil and in most bolt guns , it's a pleasure to shoot. The 06 & the 7mag offer you a wider range of bullet weights for different game and are a tad more versatile. The 7-08 that sj mentioned is good along with the 7mm mauser and 6.5 swede. There's alot to choose from and everyone has thier favorite caliber. If you can go to a local range ,maybe you'll be able to find someone to help you out and let you actually shoot the different calibers before you decide.