06 is a solid choice. He Will need a good scope that tracks good and learn how to read the wind and his turrets.
I'm comfortable to 400 yards with my tikka 06.
For me At 500 + yards errors start to magnify and things start to open up . It's a long ways. Requires practice.
I think a magnum would be better for 600+ yards on big animal like elk.

All of them do something better than the 30-06, but none of them do everything as well.