Reducing humidity with a fan: top or bottom?
Dry air is more dense than humid air, so your thinking about humid air accumulating near the ceiling makes sense. Because it's a basement, however, I'm going to assume humidity is coming through the floor or walls. Tackling the source of the humidity by letting drier air circulate along the floor and walls will probably be most effective at drying the space.

Your best bet may be to mount the fan as an intake on the bottom grate, so less humid air blows onto the floor and quickly disperses rising moisture. It would also help to open up some air space along the floor. You could achieve this by storing your items on a raised shelf or pallet. Providing this extra space for air circulation might even be enough to keep your storage room sufficiently dry without forced ventilation.