If you're looking for a basic precision rifle, you could probably expect <1MOA as box stock average.
Two of the most popular bolt guns are:
1. Remington 700 (700P probably being the most popular). This gun is offered in endless variations, with endless upgrades.
2. Savage 10FP. Not quite as much aftermarket following, however, it's widely agreed upon that it's got one of the best triggers available for an off the shelf bolt gun. I just bought a 10FCP (detachable mag version of the FP) with an HS Precision stock. I wanted a basic, not overly expensive, .308 to ease my way into precision distance shooting. I have about 5-6 different Remington 700s on my list of 'must haves', so I decided to go with the Savage to mix it up a bit.
I'm not sure if I've posted it in this thread yet, but I'm a pretty big fan of Budsgunshop.com. They've got GREAT prices and haven't treated me wrong, yet. Or, if you're not sure what you want, I'd recommend going to the store, and playing with some to see what you might like. If you can find someone, and they'll let you, try to shoot some if you can.