For me, pass the 308 or 270. I've got no use for a "Big 7."
A long time ago the Military determined that a ~ 150 gr. bullet, at ~ 2800 fps., was an optimum balance between rapid marksmanship skill development and 500 yd. effectiveness for the average adult - .30-06 M2 ball -> 7.62x51 NATO M80 ball.
... this would also include the .270 Win.
GR