Build it.... it will shoot.....
Start with a virgin action, or one printed already.
https://grabagun.com/firearms/rifles...bon-steel.html
https://bighornarms.com/product/origin-action-deposit/
http://pacifictoolandgauge.com/1406-...on-700-actions
http://northlandshooterssupply.com/actions/remington/
Barrel it:
http://northlandshooterssupply.com/b...ington-remage/
https://kriegerbarrels.com/
https://www.bruxbarrels.com/
Trigger it:
https://triggertech.com/collections/bolt-action
Stock, obviously, whatever you choose for the application. Basic BR stock doesn't need to be expensive. Can be, but doesn't need to be. Something properly bedded that fits you and go. You'll get more out of money spent on a rest and bag for it to ride in.
Last thing I'd do would be start with a factory boxed rifle then make mods to it.
The above you'll hopefully sneak into the 1500 range, but likely exceed it. But, you'll have a rifle that will shoot correctly versus a boxed rifle (Savage, etc.) that will need work to get straight. Will the savage TR shoot out of the box. Yes, of course. Let's not piss everyone off in the forum all at once.
I'd probably leave Tikka and Bargara out of that statement though as far as a boxed rifle doing what it should out of the box.