For an outhouse I would say go with a DC fan and DC LED light tube or bulbs. If you are looking more things like Pump set, then increase panels and Solar charge controller.
For using at night time you have to apply a Battery and it depends upon your usage.
We are watching a lot of Solar powered inverters that will reduce our energy costs. I am too planning to place solar panels on one of the roof, but outhouse is best in my understanding where calmness and no pollution.
Why not buy a ready made outhouse with solar panel? I have seen making an outhouse is excellent, but never depend upon others to buy and you can take some designs from the Search engines or from instructable or from gardening groups. A lot of ideas can come into your mind to build a great outhouse with solar panels.