I agree the .30/06 is a good choice. Suggesting that the .308 is better because it is potentially more accurate fails to take into account many variables, not the least of which is a broader useful range of propellants and bullet weights. The '06 set many accuracy standards throughout its long and glorious life, and it leaves little room to be sneered at today. The only reason my target rifle is a .308 is because I found a M-700 short action before I found a long, as I would have been able to simplify my logistics as I already owned a .30/06. High quality components like Lapua brass are available for the .30/06.
It would be very interesting to build a pair of identical precision rifles, one in .308 and the other in .30/06 and see if the superiority of the .308 stands up to close scrutiny. I've done some decent shooting with both rounds, and I'll bet they would end up in a dead heat. Having said that my .308 target rifle has shot the best groups I've ever shot, (in the .1"s) but then again I've never invested the dollars in a .30/06 built to that level of precision either.
As an analogy, a .22 PPC is said to be potentially more accurate than a .222, but that does not prevent the .222 rifle from being a very accurate worth while rifle to own. Neither does it guarantee an automatic advantage for the .22 PPC over any and all .222s. The rifle that wins matches on any given day is not necessarily the most accurate rifle on the line.