I really like .308, I have two.
For your purpose I would suggest a Remington 700 vsf in .308 - IMHO the most accurate "off the shelf" .308 produced.
A bolt action, synthetic stock, heavy floated barrel rifle that can compete with custom offerings costing much more.
Like they say in the ads: "That prairie dog had it coming."
I can shoot 3" groups at 300 yards with mine (and I'm not a great shot), I love it.
I use a 10-16x scope with bullet drop compensator reticle, but if I had it to do over, I would probably prefer a quality 10x fixed magnification scope so that I could always be certain of sighting in at the same magnification.
It IS a beast.
Check it out.