Either 243 Winchester or 6mm Remington as for big game hunting are excellent Antelope/Deer cartridges, using 85 to 100 grain well constructed bullets.
The 243 Winchester will meet everything the 6mm Remington will do up to approx 95%, which is splitting hairs. No noticeable difference on game performance.
My personal ethical maximum yardage is 300 yards, for any of my cartridges. Any further and I have the capability to stalk closer or I will pass on the shot.
yooper77