I'm personally fond of using epoxy for pretty much everything. It's fairly easy to work with, usually has a pretty quick cure time, is non-toxic, and it sticks to almost everything.
Depending on what you are working with, you could use either the putty sticks or the stuff that comes in a dual syringe.
The silicone and hot glue won't adhere well to some rocks, but if the surface is really rough (like lava rocks) they will probably work. The silicone takes a while to cure though, and it's generally pretty expensive.
I've never had much luck with superglue, aside from using it to glue plants to wood/rocks, but that's just me.
Also, working with slate can be tricky - some of them are "flakier" then others, and even if the glue holds, the rock might just flake apart, leaving a paper-thin layer stuck to the glue.