Savage 110 or Stevens 200 (same rifle, just with or without the accutrigger)
Very typically has great accuracy (MOA or sub MOA right from the box) and can be had for really cheap new or used. You can get them new for as little as $250 for a stevens, and used for often times under 2 bills.
And the other really nice thing about savages is they use a barrel nut that is easily taken off with a few tools and allows you to completely switch calibers in as little as 10 minutes. Want to shoot 308 today, 6.5 mauser, 8mm, .338, or .35 wheelen? Not a problem. Your one rifle can become 3, 4, 5 or more.
They really are an amazing value for a high powered rifle.
As an example, I recently got my Savage 110E in 30-06 used with a old Weaver scope for $190 from Gunbroker. Heck the scope was worth $75-100 by itself. Took it to the 100 yard range for the first time and was shooting just over 1 inch with LC ball ammo.
Shes not a looker, but she really can out-shoot me