Light-sensitive species
Realgar is the standard warning: prolonged light exposure converts it to pararealgar and it crumbles to orange powder. Proustite darkens. Some amethyst and rose quartz fade measurably over years.
These belong in drawers, not on a windowsill.
Humidity in both directions
Halite and other soluble species absorb atmospheric moisture and deliquesce. Zeolites and some hydrated sulfates lose water in dry air and lose their lustre permanently.
Sealed containers with a controlled buffer solve both problems. Room air solves neither.
Handling and dust
Softer species take fingerprints and etch from skin oils. Dust on delicate crystals is difficult to remove without breakage, so covering is easier than cleaning.
Handle by the matrix wherever a matrix exists.
A workable arrangement
Sensitive material goes in closed drawers, each specimen in its own box with its label. Everything else can be displayed, provided it is out of direct sunlight and away from radiators and exterior walls.
A cheap hygrometer in the storage area is worth more than most accessories a collector buys. Somewhere between forty and fifty percent relative humidity keeps both the deliquescent and the dehydrating species stable.