When I was in AK I scoped my 338 with a 1 3/4 X 6 Leupold. Most folks WAY over scope their hunting rifles. The 338 is what I call the 'Alaskan 06'!
One of the thinks I insist on is BIG field of view 'up close'. On the 1 3/4 setting I could place a shot as close as a few feet (which is comforting if a bear is charging)!!!
If you do not have open sights as a back up I strongly recommend you use dual dovetail mounts, if you have open sights I would recommend the Leupold Quick Release mounts.
At six power I can take any shot at ANY BIG GAME animal out to 300+ yds.
It don't get any better than that!!