Polished slate would be awful to live with, it is simply too soft to be practical. You could easily scratch it with the bottom of a rough coffee cup never mind anything harder.
If you want something polished and black then granite is the way to go.
Slate is a better product if it's split or riven and at a push honed, but not polished.
Best thing to do is go to a few stone manufacturers or stone masons or monumental masons and ask what they have available, if it's a small hearth then your likely to be looking for an off cut of some description.