What is the best barrell length for an ar15 chambered in 556 NATO with a 1 in 9 twist?

Depends. For long range shooting, you're probably not going to find one off-the-shelf with the 22 or 24 inch barrel. You can still reach out and touch something at 300 yards or more with a 16 inch barrel. If you want it to be as "authentic" of an M4 as possible, then you'd want a 14.5 inch barrel with a permanently pinned and welded flash suppressor long enough to bring the barrel length to 16 inches.