Proper Opening Moves
In The Backgammon Book, World Champions Oswald Jacoby and John Crawford recommend with both 6-2 and 6-3 moving one runner to the bar point and one man from the 12-point into your own outer table; though they concede that there another move almost as good:


  The modern play [written in 1970] is to use the six to move one back man to the black bar point and use the other to move a man from the black twelve point into your outer table. ... Unless [the man on the bar point] is hit by a point-making roll (in this case 6-1; double 6; double 3; or double 1) you will have a lot of possible returns against your opponent's  vulnerable blot; and you have lost little anyways. If your man is not hit your position is highly advantageous.


Note that Jacoby and Crawford do not recommend the modern play above with an opening roll of 6-4. 

For both 6-2 and 6-3 they regard one alternative move each being nearly as good as the modern play recommended above: with 6-3 running with a single runner to the ten point, but with a 6-2 moving a man from your 12-point to your inner board.


  With a 6-2 we don't like the running play [moving a single man from black one point to black nine point) at all, as it exposes your man to a straight 4 or 3-1 or double 2; a total of 14 possible shots.