Rose quartz is a fairly hearty stone that is not particularly prone to scratching. It is not ill-affected by humidity although any sterling silver or gold that accompanies them may be.
The biggest danger in storing rose quartz pieces is actually that it might scratch other pieces. As with most other materials, it is important to wipe down your crystal with a soft cloth. This removes the dirt and oils from the day.
Heavier pieces of quartz are best stored laying down, especially if they are hung from cloth or leather cord. Smaller pieces can be hung but should not share a hook so the stone does not scratch other pieces.
Be sure to follow specific information for mixed media pieces, or pieces that include other fine gems, enamel, or specialty metals. The rocks themselves will typically withstand most cleaning processes without ill-effect.