Quartz countertops are from man made materials and therefore more uniform. There are many brand names. You can make your selection from a book or website showing the patterns.
The biggest advantage is their durability.
Natural materials are more varied and require more maintenance but can be more interesting. These materials vary enough that viewing the slabs at a supplier location is necessary. Pattern and color options need to be monitored for best results. Do not specify unless you can physically check the current supply.
(Other countertop options are covered in the main website.)