The best opening move for 3-1 in backgammon is 8/5 6/5. Makes the 5-point, the best point in the game. Watch it on the board, then read the idea behind it.

The idea behind the move
With 3-1 play 8/5 6/5: two checkers land on the 5-point and it becomes yours. The 5-point is the most valuable point on the board: it blocks your opponent’s back checkers and is the base of a strong home board.
What comes next
After the move you have no lone checkers in front, so the game goes on calmly. Your next aim is to add the 4-point or the bar point next to the new point.
How to read the move
A move like 24/18 means one checker goes from your 24-point to your 18-point. Points are counted from your side: 24 is the farthest, 1 is the deepest in your home board. “(2)” after a move means you play it with two checkers.