I found the online Points calculator, and based on my current weight, it calculated 59 points. So - are these the points I use to maintain my current weight? Or are these the points I use to start off with to lose weight?

Should be points to lose weight. They will drop as you lose weight. When you get to goal and Maintenance they add 6dps.

Those are the points you start off to lose weight along with 49 weekly points. Check the calculator often after losing every 5-7lbs because your daily points go down as you lose.