Can the 82gr Bergers be seated to magazine length? I see they're not a VLD design, but that's still a pretty long bullet.
As for your bullet choice, the 69gr Sierra works fine at 200 and 300 yards, though it takes a bit more wind than a 75 or 77gr bullet on a breezy day. The 80s are truly at their best seated long and at long range. If you're not shooting past 200 yards, stick with the 69s; they're inexpensive and shoot well.
If you're looking to shoot the .223 AR-15 across-the-course to 600 yards, the most common approach is to use something like the 69-77gr bullets at 200 and 300 yards and then either a Sierra 80, Hornady 75gr Amax or a similar bullet at 600 yards. Depending on your range and wind conditions, you could do well to shoot the 77gr Sierra Matchkings or the 75gr Hornady HPBTs all the way back too.
And don't stress about load development and bullet choice too much. Just find something that works well and reliably and make a bunch of it. Front sight, trigger squeeze, breath control and follow-through are still the most important factors to focus on.