They are all stone, which makes them hard, heavy. They are natural products, which means there can be variations in color and pattern, and sometimes what you see in the display/sample is not exactly what you get delivered with granite and marble - you should view your slab. Quartz is predictable with its color and pattern so the samples are what you will get. All come in a wide range of colors, and patterns.
Granite and marble can be stained by oily or highly colored foods. So both require resealing every once in a while (every 5 years). Both are relatively heatproof, and they won't scorch - can withstand heat temperatures up to 1200F. Quartz does not require sealing and is heat-resistant up to 300F.
If you are choosing between granite and marble - granite resists impacts and scratches better. And it is resistant to acids like tomato juice, lemon juice or vinegar. Marble is calcium carbonate, just like chalk, but in a compressed and crystallized form. So acids can etch the surface permanently. (And it will fizz, just like chalk in vinegar.) It also can scratch more easily. Some marbles have very little pattern so stains and marring stand out more.
Practical considerations aside, marble has a look that is possibly more elegant and luxurious out of the three stones. It has extremely fine crystals, which create a snowy or satiny look. And the colors and patterns can be quite dramatic. Granite tends to have larger crystals, perhaps the size of peas or rice grains. This creates a coarser, more sparkly look. And while granite comes in a range of colors and patterns, that range is probably narrower than for marble.
Granite is recommended for hard use areas like countertops. Marble is higher maintenance and used more often in bathrooms or low traffic areas. Its one advantage may be in appearance, but that will depend on the owner's taste and the kitchen's overall style.
Quartz or "engineered stone" is less porous. It is made of quartz powder that is fused together at very high heat. Unlike granite, it resists stains and doesn't need sealing. It comes in patterns and colors that mimic granite very closely, but it is totally predictable, and more uniform than real stone. It also comes in colors and patterns not found in nature, like bright blue so you have a vast choice when it comes to design options.