Remington 700 action -$350 or you can buy a used gun for 500ish and sell the barrel and stock.
Bell and Carlson stock- $270. Great value for the money. Same stock as Wby accumark.
Premium barrel-400
Action trued, barrel chambered, fit , crowned etc by gunsmith for several hundred.
That puts you under 2k, probably about 1500 for something that is going to shoot great, you can pick a custom twist and length , add muzzle brake, add jewel or timney trigger, add fluting, cerakoting, etc if you desire.
The majority of your accuracy is in barrel , then stock stiffness and square action come into play some, but for the most part it's about the right load for the right barrel. Buying Kreiger, Lija, Rock, Bartlein, Broughton... they are all going to be better than what you buy off the shelf. For that matter, the B and C stock is better than the majority of factory rifle stocks.
In essence , I think you can do better for cheaper to equal price by building