Meanoldman;
I've got a .338, on an older Tikka Whitetail Hunter platform. Mine wears a Zeiss 3.5-10X mil-dot, which is out of the budget range you gave me. But, you also didn't give us a yardage for medium to long range either. Therefore, the Zeiss 3-9X that's available for the top end of your cost number might very well do the trick very nicely for you. If that's not possible, look to Leupold or Nikon IMHO. However, do reserve the required funds for good mounts. I use Talley's almost exclusively now, I find it's money very well spent.
900F