When you are referring to slate, I hope you are talking about getting a high quality, fairly expensive, precisely cut product from a reliable flooring supplier? The reason I ask is that all the big box stores in my area sell a horrendous, extremely low quality slate that they import from India. The stuff looks beautiful, and I have used it extensively on fireplace surrounds, but it would be a disaster on a floor. The stuff is typically radically out of square, with extreme thickness variation ( literally, I have pulled tiles out of the box that vary from 1/8" to 5/8" thick) , and it can flake easily.
I have done very little real slate on floors, and when I did it was about $6-7 sq. ft. for material. I have done at least a dozen kitchen floors with a high grade porcelain tile that looked exactly like slate. This stuff was under $2 sq. ft. looks great, is rated for commercial use, and easy to use. No matter what you decide, take a look at the bright orange "Ditra" underlayment. It's the only thing I would ever use. Good luck on the project.