The fact that you do not reload hurts this quite a lot. If you can not reload, then I have to say 300 win mag and have done with it.
Now if you could reload, I would say 25-06 with a 115gr berger hunting vld. This would be good to go out to right about 600 yards. But then, You would probably Have to reload. A lot less recoil and drama than a 300 win mag
Lots of good answers posted,
Have a good one,