Marble is a metamorphic rock composed of recrystallized carbonate minerals, most commonly calcite or dolomite. Marble may be foliated. In geology the term "marble" refers to metamorphosed limestone, but its use in stonemasonry more broadly encompasses unmetamorphosed limestone. Marble is commonly used for sculpture and as a building material.
Quartz, because pigment can be added, is available in a much wider range of colors for you to consider. The way the countertop material is formulated gives it the appearance of natural stone such as granite or marble. The bottom line in appearance is that if you want natural stone, quartzite is your choice.
Soapstone is a talc-schist, which is a type of metamorphic rock. It is largely composed of the mineral talc, thus is rich in magnesium. It is produced by dynamothermal metamorphism and metasomatism, which occur in the zones where tectonic plates are subducted, changing rocks by heat and pressure, with influx of fluids, but without melting. It has been a medium for carving for thousands of years.
Travertine is often visibly porous, giving it a more natural, textured look. However, when sanded down and sealed, travertine tiles are smooth and suitable for flooring or as shower tiles. This stone is relatively soft and absorbent, so it requires a few coats of sealant to prevent debris from penetrating the stone.