RE: 22-250 range?
That Remington is a 1in14?? Correct?? You will need to shoot the lighter bullets for best accuracy(IMO). You can try the heavier bullets but they may not stabilize. You should be good up to 50 or 55 grain.
As far as range is concerned, I would say 300 to 500 yards if there is not a lot of wind. A little farther if there is no wind. I can effectively get 600 yards out of mine but I have a 1in8 twist and I shoot the 75's.
Try the Black Hills ammo. I have seen some great groups with the Black Hills ammo. Tom.