If you do not reload, I would recommend the 300 win mag. much better selection of premium ammo available and even custom loaded from Black Hills.
The 300 WSM
is great cartridge also and you can get in the Savage or the Winchester Coyote (both under $600). Only problem is limited mftr factory or premium ammos at this time compared to 300 win mag.
Sendaro or Savage would be the way to go in the 300 Win.
Either one, just have trigger worked one, action bedded if Win or Remington, lap the lugs and check crown. All for under $200 max. Should work great and be .5-.75 MOA gun if you check different ammo out to find what your gun likes best.