There's a great deal of "all of the above" in your options. Most of the difference depends on WHERE you're going to hunt, moreso than WHAT you're going to hunt.
I live in the densely wooded eastern mountains where the .308 is superior to the others because it's more efficient with a 22in barrel, it's lighter because of reduced length allowed by shorter action/barrel, and controlled-expansion bullets are more reliable due to lower velocities (than the other two options) at our typical ranges. That said, I tend to only use my .308 for Moose up here. My 30-30 is obnoxiously superior for hunting these ridge-runners.
However, if you live in more open plains...I'd pick the .270 for the flatter trajectories and reduction in recoil over the 30-06.
If you lived in a mixed environment, or want a rifle that is not as niche as the other two... go with the 30-06.