[F]I need suggestions on what kind of transition threshold I can installed between slate & ceramic tile to stained concrete.
Thanks!

You can try forming a groute transition or a commercial glue in place metal transition. Normally the glue in place transition is installed with the tile. If the tile is already installed you can try cutting off the glue tab(s) on the transition and using something like PL Premium to glue it in place.

If you want a sharp edge try browsing in the floor aisle at the home store. Look for simulated wood, vinyl or metal transition strips. Most all would have to be glued.