Have you ever seen those little carved animals that come from Mexico? You know, the pretty striped stone that also makes nice bookends, and even counter tops. Onyx is quite common and there are many varieties. I have some honey, cherry, and regular brownish stuff. There was a deposit near Mayer, Arizona that was un-earthed when they carved the freeway. While the remaining deposit is on private property now, areas around Mayer have some interesting onyx relatives still available for collecting.
The first cabochon I ever completed was common onyx, and I'm glad it was as opposed to Jade or chrysocolla. Why? Because jade and chrysocolla can be tricky to work with, and may have discouraged me early on. Onyx was easy to shape and took a high polish with minimal steps. (100, 220, 600, and cerium.) I highly recommend working with onyx as a first material for budding lapidarists.