I just went through the same dilemma. .308, .270, .30-06, 7mm RemMag, etc. After a month of going back and forth, asking everyone I know that hunts, scouring numerous message boards and reading a bunch of articles I came to this conclusion...as someone new to hunting and rifles (I own other firearms but have never owned a rifle, never been hunting) it really isn't going to make a huge difference what you go with.
I went with the .30-06 simply because of the greater variety of ammunition available in regards to bullet weights. .30-06 is probably also the one caliber where you can find cartridges in literally any shop or hardware store no matter how remote or off the beaten path.
I ordered a Winchester Model 70 Extreme Weather SS yesterday in .30-06. I've had some tell me I should have gone with a .270, other buddies who own .308's said I should have bought a .308, while others have chimed in and said the .30-06 was a great choice for someone who wants just one rifle and one caliber to be able to grow with and hunt literally anything in North America. I have no aspirations to do any long range hunting, either.
After all the research and reading and asking other's opinions I came to the conclusion that it really doesn't matter for someone new to rifles and hunting. But take what I've written with a grain of salt because like I said I'm new to rifles and dont even have the rifle in my hands and haven't shot it yet. But I think many of us get too caught up in the smallest of details and tend to lose sight of the big picture. All of those calibers will do what you want and the gear you end up with is almost certainly more accurate than we are as new hunters.