First, let's talk about leather...
Leather comes in several different types. There's cowhide,
lambskin, suede, buckskin, etc. -- a lot of variety. Each type has
different qualities: thick, thin, stretchy, etc. Super thick leather
will not work very well for embroidery. You want something
more malleable. However, super soft and thin leather, like some
lambskin, may actually be too delicate to hold up. A medium weight
leather will be your best bet.
Note: Faux leather is very different from the real thing, and can
handle a much wider variety of embroidery designs. More on this