ANY of the 3 = great for anything under 200 yards....
My picks for the 3 if hunting deer sized game =
1)270
2)308 or '06 (they are pretty much the same)
my pick for the 3 if hunting something little bigger (example elk)
1) '06
2)270
3)308
But seriously, to put them on a scale, lets say the '06 is a 10, then the 270 or the 308 are like 9.999999 (ALMOST a 10), they are idential in knockdown power / accuracy for shots under 200 yards.
To make your choice a little easier, Go with the one that has the cheapest ammo, like the 30-06 (I buy softpoints remington 180 gr from walmart for $12.50), Gander sells a tint of .308 not sure how manny rounds, but they are 150 gr FMJ primarly for practise for 65$ (I think there is like 200 rounds in the tint)..... now .270 ammo is the most expensive one of the 3, a box of them is usually around 20-24$