Store with the valve closed to prevent bacteria and bugs from entering. For any freshwater system you want to keep outside air from getting into the "clean" area.
In winter, store without water to prevent freezing. (Once it's drained there won't be enough water to freeze that will cause any problems. When water freezes it expands, causing things to break, but with just a small amount in the bottom of the tank there's room for it to expand.) During the season it's up to you. Some store water in case of emergency, I prefer to keep mine empty so I can put some fresh water in before leaving so we can flush the toilet, then fill it up just before we arrive at the boon docking location. If we'll have fresh water then I rarely keep more than about 5 gallons in it.
Rich & Yvonne
2006 Safari SE -Dora-
2004 4Runner SE