5 year old buck +
One man's opinion, I love a .270 because it shoots quite flat out to 200 yards and is more that enough to drop a deer or black bear in it's tracks. The .308 is probably just as good. The 30-06 is a bit bigger than what you need for most "eastern" hunting in my opinion, but certainly a good rife. The man pulling the trigger is really the biggest difference maker, no matter which gun you settle on.
The .270 is another great choice for a young first time hunter.
The .308 is actually is a actually a step above the .270. It is one of the more common calibers that military snipers choose. Very accurate, flat shooting, and not a shoulder pounder. I have killed many deer with mine out to 250 yards.