Good stones for building dry walls have relatively flat faces, at least 2 angled edges and consist of limestone, sandstone, and granite. This type of wall relies on friction and gravity to hold together and ranges in height from 12 to 24 inches. A concrete foundation is not required, but it should rest on a firm footing and seem to grow out of the ground, rather than sit on top of it.
Once a substantial foundation and gravel footing is in place to prevent settling and cracking, a mortared wall is easier to build than a dry stack wall. The gaps between the stones are filled with mortar, making stone placement less critical. A wider variety of stone is also available and more styles, from formal retaining walls to relaxed looking, free standing walls that appear to be dry laid.