I don't know a thing about gems, and I'm asking out of curiosity: how are facets made? Is it through cleaving, or grinding/lapping? If you already have a machine that does what you want (with you at the helm), I would think automating it would be the place to start.
I'm guessing that it is no so much a milling machine with cartesian (X,Y, & Z) motions, as a machine with polar motions (rotating your stone) in two planes. And then some way to advance your cutting/grinding head. Am I even close or am I way off base?
I can't imagine that speed is your biggest concern-if not, then PC control from Windows becomes a reality (parallel port contol under Windows has a limited maximum pulse rate).
Assuming that this is good for you, you can interface directly from the PC port to step+direction stepper drivers: I like the Geckodrives.
Let's say you need three steppers and the little NEMA 23's are OK. If you were to opt for the Geckodrives, you would want bipolar steppers. I have some that are rated at 5V, 1A per phase. Let's use these ratings. What does this mean in terms of other hardware?
Geckodrives require a power supply voltage between 24 and 80 VDC. In addition, good high speed performance requires that the power supply be be 4 to 20 times the rating of the stepper. Some typical power supply outputs are 24, 36, and 48 VDC-any of these would work.
Our reference motors have two windings (phases), so worst case (both windings on at the same time) we are talking 2 amps (1 per winding x 2). NOTE: this really isn't a normal condition-both phases energized at once-but if we design for worse case nothing will go up in smoke.
You could find either one supply capable of supplying 6 amps (3 steppers * 2 amps) or three separate 2 amp supplies. Again, a little overkill, but you are erring on the safe side.
The basic G201 stepper drives are $114.00 each. Do a little eBaying and factor in your power supply costs.
What else? While not strictly necessary, end of travel limit switches (set up to kill your drives if triggered) will keep you safe. These can be mechanical, optical, magnetic, etc.
Also, some sort of "home position" switches to tell the PC that the machine is at a know position: all other motion is relative to that place.
Oh, the G201s are microstepping drives (with a fixed factor/multiplier of 10). So, the reference steppers are rated at 1.8 degrees per step or 200 steps per revolution. Using the G201 you would see 0.18 degrees per step/2000 steps per revolution. Figure out what this means in terms of movement on your machine.
Not precise enough? Use toothed wheels and belts with a reduction ratio designed to get the resolution you need. Example 3:1 reduction would mean 6000 steps per revolution.
Software? Hmmmm. I don't know if any of the typical CNC stuff would be what you would need. I suppose a good description of your machine would be needed to determine that.
BTW, did you know that there was a "Glass, Plastic and Stone" forum? It may be the better place to post, if for no other reason than it is for people with interests similar to yours.
I don't know if any of this helped, hopefully it did.