FN Winchester 70 Featherweight, shoulder it one time and you will understand why
Love that gun, not quite as tight shooting as my Tikka but I adore the CRF action, the top of the food chain ergonomics, and the wood work is superb. I found mine for well under your price range. Mine is a 308 and it is a long way from a shoulder bruiser, the rifle soaks up the recoil remarkably well and the 308 is very big game capable within 300 yards. They make it in some flatter shooting calibers too, I would like one in 270 WSM which is the flattest shooting caliber I have ever owned, and well below the 7mm Rem Mag in the recoil department.