The 308 with it's small case does not drive the larger .308 bullets (180gr and up) as well as some others....

30-06 is a fine place to start, 300WinMag is lovely, 338WinMag even better....

IMHO, more is better depending on your ability to:

(1) Afford it,
(2) Get your rifle set up PROPERLY, and
(3) Handle it.

[Many cartridge myths likely to follow.]

EKM