What are the most common opening move for 6,2 and 6,3?
It seems the logical move is to take a runner and move 8 or 9 pips. However, after playing a lot lately online I notice people also like to move into the #7 position with one runner and move 2 or 3 with the remaining runner. While it seems risky, I also think that unless your opponent rolls a 6,1 or 6,6, they are opening themselves up more than you are opening yourself.
The exception of course would be if you were second to roll and your opponent has other crippling rolls available depending on their first roll.