As a starting point, size 3 level fluorocarbon tenkara line, the length of the rod (a little less for narrow streams, a little more for lakes). If there is a bit of a breeze you might want to fish with a 4.

Furled leaders will cast more easily - largely because they are almost universally heavier, and a heavier line is easier to cast. It is also harder to hold off the water's surface. To me, the light line you can hold off the surface, minimizing drag, is the essence of tenkara. Since you furl your own leaders, I know you will make a tenkara line. I would suggest you make it no more than 12' and lighter than any you've ever made.

Kevlar and UNI-thread will absorb water and get even heavier. I would treat them with floatant, not to make them float (because they should be in the air not on the surface) but to minimize water absorption. The other alternative is to make them extremely light and plan on the water absorption to give them the weight necessary for casting.