I have a vertical hard drive dock I use occasionally. I just store the drives on a shelf when not in use.
Dust infiltration should be minimal, drives have little air filters on their ports (unless they are sealed drives, in which case, they are sealed)
Static is more of a concern with the exposed PCB on most drives. But enclosures should all cover that up pretty well from being touched.
My rule of thumb is always to touch your hands to whatever surface is touching the component to be picked up, then, while holding the device, touch the next surface it will be in contact with with your hand again before letting the device touch. Should equalize large potentials and avoid shocking components directly. Can't say I've lost anything to date to static. Most of my component failures were during the days of capacitor plague.