* Horse-drawn carriages: Most horse-drawn carriages were right-hand drive, and early automobile designs were heavily influenced by carriage design. The driver sat on the right to better control the whip.
* Passing on the left: In many parts of the world, passing on the left was (and still is) the norm, making right-hand drive a natural fit for overtaking.
So while you can't point to a specific "first" of either type, right-hand drive was more prevalent in the earliest cars. Left-hand drive gradually became more common, especially in the United States and in countries that adopted the left-hand driving rule.