fairly light, but somewhat thicker and easier on the hands for use by little hands.
Commercially available kite line for kids kites is either light, and hence thin (burns, cuts, ouch!) OR it is thick ( too heavy for light pulling kites). It is very difficult to get both good qualities without any of the down sides.
Cotton thread seems to be a reasonable compromise. It is thin and light, but quite a bit softer, gentler on little hands than commercial threads.
If you don't want to wind lots of line sets individually, you can always do what Tony Rice taught me years ago.
Cut a bunch of rectangular cardboard pieces (to be used as winders). Buy a large cone of cotton thread ( the sort used on overlockers, etc). For each child, give them a cardboard winder, hand them the end of the thread and tell them to run for 10 seconds. At the 10 second point, cut the thread. The child then winds up however much line he/she has managed to get in that time. Fun and simple.