Eye protection, also extremely important. You only have one set of eyes. Flying chips from the rock can change the way you see things forever if you don't where safety glasses. Some shock resistant gloves protect the hands from the vibration and abrasions from sharp stone chips. Stone has been carved for a long time without much equipment being necessary.
Softer stones are, of course, easier to work with.
It comes in lots of colors, and is the softest stone that will hold together well enough to be worth carving. Restaurant supply outlets carry butcher's gloves that will protect somewhat against a slicing wound, which are common among those who carve using the hand as a vise. Whenever using electricity and water together, make sure to run the power through a ground-fault interrupter, which cuts off the power when it senses a short. Steel files will work on this material for smoothing out, as will any sandpaper. You'll save time if you start by roughing out the shape with a saw, or you can just start whittling.