There are two categories, service rifle and match rifle. I'll skip match rifles, because there's literally too many variables to talk about.
Anyway, the service rifle is the most common platform I see in Texas, and the most common and easy to shoot (good scores with) is the AR-15. Everyone uses the same basic gun, because, well, you have to by the rules. 20" barrel, iron sights, 4.5lb trigger pull, etc. The most common and probably best setup you will see is: 20" dcm contour barrel (1:7-1:8), .036-.046 rear hooded aperture, .052-.072 front post, geissele national match service rifle trigger, free float A2 hand guard, and a 2" leather sling.
The 308 is a BEAST to shoot 88 rounds with, and while it may have some advantage at 600 yards, there are more disadvantages overall. Stick with the AR15...
Your best bet is to call up John Scandale at Keystone accuracy, Lee Wells at Accurate & Reliable, or Robert Whitley at AR-X (6mmar.com). They are all high master shooters, great gunsmiths, and will answer any questions you might have. They also build some sweet match rifles on the AR platform, so if you decide to go that route they can take of you as well.