All of our borders are layed on a granite gravel base for stability and to raise bottom border flush with grass line. The two types of natural stone are moss rock and chop rocks.
Moss stackers are typically two courses approximately 6″ high. Thicker stones are available. Chop rocks are either tan, gray, or limestone colors. Usually single course with typical thickness at 4″ to 5″ and same on depth.
Another option is to place a single moss rock boulder in varying increments to change the elevation. Also it is very common to add additional courses on corners to adjust for the elevation.