If you do use a chop saw, make darn sure it is tight to the fence to avoid it sucking in at a significant speed that is sure to wake you up, and be careful once it is in half as well, it can launch pretty well if you are not careful.
And can't say enough, don't breath vapor/fumes from friction heat if you do dry cuts on living rock.
As for bits, yes, masonry bits, they are cheap, and oversize slightly, 3/4 bit for 1/2 rods if that is what you are using.