Dirlling in marble

I need to mount a piece of marble overheard that is about 2×36x5/8. I want to use a couple of screws and need to know the best way to drill it and not break it. I have a drill press and I know I need to tighten it gingerly, but any other suggestions? I figure 3/16 is the nearest larger size I will have to use and the bit is the biggest question I have (diamond tip?).