I think you should spend a little more on a better needle driver to start. Straight up, the kit ones are shit. Try something like this. They are flimsy and are nothing like what will actually be used.

As for being left handed, although there are left handed needle drivers, they are seemingly hard to come by. From what I've been told by surgeons, they barely see them. I suggest learning to work with the needle driver in the your right hand. Even if that means sitting around opening and closing it. Although you probably should be able to drive a needle with either hand, it is more commonly the right hand doing it. With that being said, you should be comfortable with it in either hand.

I suggest this video. It goes through each knot style that you will need and I believe he does a good job explaining.