With your budget there is a plethora of high quality and accurate rifles from which to choose - FN 'Winchester' 70, Savage 11/111, Weatherby Vanguard S2, Tikka T3, TC Icon, Browning X and A bolts, etc. Handle as many as you can - preferably back to back at a well stocked gun shop - and see which one fits you best. Better yet, see if you can fire some of them at your local range before making your selection.
Let us know what you select. And post pictures of the rifle and groups. Remember, some of us are living vicariously through your rifle purchase.