Depending upon the altitude where you will be shooting, you can stabilize heavier bullets with a 12 twist, but Mudrunner is correct that the 185's are about ideal for a .308 (though I would recommend going with the Berger 185 Juggernaut). The Sierra 175 Tipped Matchking is also worth a good look. For the kind of long range shooting I do with my .308, though, I can't afford to shoot many Bergers. For now, I shoot the Sierra 155 Palma (2156) bullets out to 1000 yards and just live with the extra wind drift.
I have a Remington 700 VS in .308. It has been wonderfully accurate from the day I took it out of the factory box. It is a solid 600 yard rifle, but leaves a lot to be desired beyond that. The .308 really doesn't have adequate case capacity for long range work and needs some help to get there. A 30 inch barrel with a 10 twist (perhaps even a 9 twist) is a good place to start.
Because of the ease of re-barreling, Savage type rifles definitely have an advantage. If you have your heart set on a Remington 700, you would be wise to shop carefully for a used rifle and have a good barrel put on it, with the proper length and twist.