Bud's Gun Shop has a new Savage 10F/P HS Precision .308 for $660 delivered. That leaves room for a decent scope and maybe a little for some ammo. They also have the Remington VLS .308 in a bedded laminate stock for $767 delivered.
I would say a Rem. 700 SPS would fit the bill just fine. Mine shoots .5 moa with out much problem. I have shot one group .5 at around 200 yards. Lucky i guess. But the action cant be beat for the price and the upgrade ability is unbeatable.