Sometimes matrix actually may add value if it allows the specimen to sit nicely without having to use a stand. To me, natural breaks are not really damage. Sometimes during late earth movement, entire sections of vein or linings of crystal pockets have been broken loose from the wall rock. They often appear as plates of crystals. After more than 30 years of looking at quartz, you might think that I would get bored.
Artists know the quality of aesthetics in mineral specimens better than most collectors.
I look for unusual features on any specimen, such as crystal form, crystal shape, clarity, position of the various crystals, display potential to show a particular feature, and if there are any other interesting associated minerals present, either on the surface or as inclusions. It will be worth considerably more if it does not need a stand. A cluster with points that create a center of interest is very pleasing to look at. This is a rather difficult characteristic to get a handle on. We do not normally think of quartz crystal as being scarce, but certain forms, habits, and inclusions are.