Hitzy said:Savage 12BVSS or 12 Varmint Low Profile. $700-$750, already in a good solid laminate stock, accutrigger is already there, just need a base, rings and a good scope.
Speaking from experience, so-called pillar bedding job in this model leaves a lot to be desired. Its just a couple pieces of thin steel tubing in the wood stock - no bedding compound. These rifles can be good shooters if you accept that you have to get them custom bedded.
Mine shot 1" groups out of the box with lightly loaded 55gr ammo, but groups opened to 2" when I used a heavier bullet loaded at higher pressures. After bedding, the both the heavy and light bullets would group .5" -.75".
If you don't want to go to the expense of custom bedding a rifle, you should stick to the brands and models that come with the HS precision stocks with the aluminum bedding block, and even some of those could use some bedding compound.