How can I mount a polished stone to wood?
Epoxy resin
I love the stuff for the same reason John Vukelic's answer does so I would recommend it here as well. Even some of the cheap 2 parts should work perfectly fine for this. It is very good at bonding different material even when the surfaces are not perfectly mated.
The two parts about Gorilla Glue that need to be cautioned here is that it has expansive properties and is (as far as my experience with it goes) not a clear product once cured. These can both be mitigated with proper clamping and proper application.
Prep your surfaces
There are infinite ways I imagine that you could place your rocks so it would be hard to cover all angles of advice here but there are a couple of things I want you to look out for.

Try and mate the surface of the stones and wood as best you can. Glues will fill the gaps but if you can keep the spaces as small as possible you can help prevent air and moisture pockets which could lead to complications in the future. Again... not a huge risk but worth putting in the time.

Avoid crevasses where moisture will sit. Follow up from the last point be sure there is few places for water to sit or seep in. Depending on where your stick gets used and lives you don't want moisture build up to weaken the wood underneath. The wood is going to fail before the glue does.