Quartz
Quartz is man made and as such is a very durable, strong option for counter tops. Manufacturers are getting better and better at making quartz that looks more like a natural stone. Quartz does not need the constant attention that marble needs, yet still gives an appearance of a clean and clear counter.
Marble
Marble is beautiful. It is luxurious looking and lends class to any kitchen. Keep in mind though, marble is a natural stone, and is porous and does stain! If you are choosing marble, you are going for appearances over durability, as marble needs to be maintained. It needs constant sealing to help keep the pores from getting clogged.
Granite
Granite is beautiful, and no two cuts of granite are exactly the same. It is not as temperamental as marble, but not as maintenance free as quartz. Granite can stain and can chip. Granite comes in a plethera of colors and there is a style to suit all personalities.