I've got a giant fuyu and love it. The fuyu is self-fertile and will polinate it's own flowers (with insect help). If you want seedless, you can insect net the tree, though air moved pollen can still polinate though far less likely.

I have two persimmon trees. The first tree produced seedless fruit until we got the second tree : ) Now all the fruits have some seeds, but it seems like not all of them have as many seeds as they could have. I think something like partial pollination is going on.