A couple of questions and/or comments:
1. Are you replacing your existing counter tops or laminating this material over it? If replacing, then you'll need material that is at least 1-1/4" thick for structural strength. If laminating, you'll have to remove your sink and reset and resealed against leakage.
2. Most kitchen cabinets are 24" deep, and the counter tops are 25" deep in order to overhang the cabinets. Your calculations on how much material needed needs to take this into consideration.
I found a website for you to start your research. This site is a designer who has worked with slate, and explains some information you should consider.
The Kitchen Designer - Journal - Kitchen Countertops - Slate, Yes,*Slate!
I would do additional research using the Google phrase "slate for counter tops"
Personally, I prefer granite from a durability standpoint, but to each their own. If you plan on doing the work yourself, make sure you have all the details worked out before committing yourself to spending any money. Just because something is a deal, doesn't mean it's the best for a particular aplication. Also, from a resale point of view, I would stay with a more traditional material that would appeal to more buyers. Granite, solid surface materials like Corian, and traditional plastic laminates with plain and bevel edges are very safe for resale.
I install all of these materials, and in 30+ years have never seen slate in a kitchen or bath for a counter top.