Quartz is an engineered stone that is the strongest and most durable stone in the market.  This stone is almost maintenance free and do not require sealing.  Presently, Quartz is the most popular choice of stone countertops for kitchens and baths because it is not porous and easy to clean.

Marble is a soft natural stone that is highly porous therefore they are easily stained.  Acidic liquids and cleaners can leave etches or blemishes on your marble countertops.  Marble also chip and scratch very easy so you have to be extra careful when using them.
Marble is very high maintenance and require a lot of sealing.

Granite is strong and durable natural stone that is the best choice of natural stones to use for your kitchens and baths countertops.  Being natural stone, no two pieces of slabs(sheet) are identical.  Each slab (sheet) of stone have their own charm and characters.  You get the REAL beauty from nature.  Granite will require to be seal on a regular basis.  Certain granite will require more sealing than others. Granite will stain if you do not clean them right away.   Once the stain penetrate into the stone, it's very hard to remove.

For all stone countertops, just a mild soap and water will do.  You can also buy stone cleaners and Sealers from Home Depot at a very reasonable price.