Just as another data point, diamond drill is what you want. If they (Rio Grande or other lapidary supply) have the Crystalite "Triple Ripple" drill in that size, use it as it tends to drill a little better. Get a couple of drills as they can be burned out by the novice.
Work with the stone immersed in a wather bath or with copious water flowing over, and peck frequently to get out the "swarf" (mud). Glue a sacrificial stone or have plaster on the back of the hole if it's a through hole to eliminate chipping or drill from both ends.
You can do it with a wire and SC grit too but it's slow...
To polish, use some copper wire and SC grit or diamond.