.270 and 30-06 is akin to Chevy v Ford, just so you know.
My family shoots .270, great flat trajectory with a smaller grain bullet. Great for deer, can handle elk but you need a well placed shot. 30-06 is heavier, great gun and more then enough for elk and moose. For bear either will do if you place the bullet well though a 7mm is better just in case you only get one good shot. Problem I hear with 7mm (not having shot one) is the kick tends to cause flinching and jerking on the trigger so accuracy is a mess.
As for the .308, can't say though if you go with the 30-06 you won't have any regrets, certainly considering the availability of rounds.
Scope, I have a Leopold. A little more expensive but worth it. With scope, what ever you go with find a good gunsmith for the mount. More then anything a sloppy mount will cause you confidence problems.
Good luck and post pictures of what you kill. I brag that my family owns the largest set of 2-point Mule Deer horns ever taken. 30" spread. If I knew how to post pictures I would post them. If someone knows how I could email it to them and they could post. You won't believe it until you see it. Taken in the Ponsigont, Southern Utah back when they grew real Mule Deer.
Boo