Hopefully this coming weekend I will put mine together and post pics.
At first take, Salt Box Style roof would be the option I would use given your chosen arrangement. Something like this (the black line is the ridge):
Looking at your original pic, it seems like you have created 3 unique areas with your fencing arrangement which create roofing difficulty.
One option would be to simplify that by moving the fence line to eliminate one of additional walls/slopes/corners, maybe by doing something like these (the black line is the new fence):
You could then potentially use a gable roof like this (black line is the ridge):
Some ideas
If you want to get complex or hire someone, you could really break the roof down into "zones" with a different slope/direction for each zone to move water where you want. This would be a lot more difficult and take a lot more planning.