We are designing a master bath for a our new house, and would like to use some type of a black stone on the floors, walls and vanity top. Should we use marble or granite?

First you need to determine how often and how heavily the bath will be used. Black marbles are typically soft, easily scratched and sensitive to acids; they are also easier to repair than granite, and less expensive. Granite, on the other hand, offers more resistance to acid, is much harder, and therefore resists scratching, but is more expensive and difficult to repair when damaged. If I were you, I would consult a stone expert before making your final decision.