Argh! I had typed out a lengthy reply and managed to lose it.
I remodeled my house 3 years ago. I had never touched any projects (tilework, painting, etc.) before. I tiled my kitchen floor first (18" porcelain), then my bathroom floors/walls (12" granite), and lastly the kitchen backsplash (12" marble).A few thoughts from my experience and research:
Porosity and flatness - Is your slate polished smooth or the typical uneven? Depending on its quarry of origin, slate can be relatively porous, so you'll have to make sure you keep it sealed well. However, slate can wear down far more than other types of stone through its natural aging process. Outside, you won't notice it....but walk barefoot in the house, and those little bits of stone might be more noticeable. that, and when it wears down, you lose your sealant protection at that point, so you have to be doubly vigilant about keeping it sealed.
Also, when you spill something and it dries on that unevenness, sometimes it can require a lot more elbow grease to scrub it off compared to a flat/polished surface.
Deflection - Natural stone is more susceptible to fracturing than ceramic or porcelain (porcelain tile is fired in the kiln several times, which makes it more durable than ceramic, and would be better suited to the high traffic/impacts in the kitchen). Because of this, the tile institute recommends you use the L/720 test, which involves different variables: the thickness of your subfloor, your truss depth, space between trusses, and how long the truss span is from the I-beam to the foundation wall. Your existing subfloor could simply be a single 1/2" plywood layer, or it could be thicker. If it's too thin, the tile institute would recommend you put down additional backer board.
Either way, I would recommend installing at least 1/4" backer board right over that existing vinyl (which is what I did) and screwing it into the subfloor with the special screws on 6" centers to help the mortar bond the tile to the underlayment (backer board). Simply slapping mortar onto plywood or an existing vinyl floor will not bond nearly as well, and would likely have issues down the road. (you only need 1/2" backer board when installing on walls, unless your L/720 deflection ratio has too little existing subfloor and too much deflection).
Don't let the above reference freak you out when you find out that your house is nowhere near the requirements for the deflection for natural tile. Typically, unless a home is built specifically for a natural stone floor, they usually don't have enough underlayment installed. As a result, many homes have had natural stone tile installed that don't technically meet the requirement without problem. HOWEVER, there are also many homes where lazy/untruthful contractors have cut corners and installed the tile on floors without adding enough additional underlayment to meet the deflection criteria. Result: cracking grout lines, mortar breaking up, and actual cracked floor tiles. Because of the risks, I would definitely add enough underlayment flooring (if necessary) to get at least somewhat close to the L/720 deflection. (google it for the equation/ratios to plug your numbers into).
Also, because of the wear concern mentioned above, I would recommend a different natural tile. I love granite, and you can actually get some variety (not nearly as much variety in tile as you can in countertops), but might need to search around on-line for some great deals even after paying shipping. Just remember back to the earth science days when you learned that granite is the second hardest mineral on Moh's scale of hardness after diamonds, so you'll need a new diamond-tipped blade to cut the tile. (and forget about drilling holes in it to mount things, unless it's a diamond-tipped or tungsten carbide-tipped bit). And some granites (like black) are naturally non-pourous, so you don't have to be as worried about things staining it.
Seal Before you Install - speaking of things staining tile, I would recommend that if you still are dead set on slate, seal your tiles before you install it. That way, when you go to grout it, it isn't going to matter if when you get some grout on the tile in several spots that you didn't notice until after it dried and left a nice little stain (even if you buy the bigass pastry bag kit like I did). Same goes for the mortar that you might get onto it.
Grout spacing - I don't know about you, but when I think of a grout line that's just 1/16" or 1/8" thick, I think that's waaaaaay too thin. However, when you actually install the tile and then grout it, to me at least, that grout line appears bigger to the eye when filled. So find some tiles that you like the grout width for, and buy a few bags of tile spacers to hold up to the line to verify which grout spacer is the right size.
Practice! - If you've never done this before, it's worth it to use some scrap tile (or even a few full tiles) to practice with. Far better to spend $20 on a few extra tiles and an hour to practice your tile work than install 100 sq ft and THEN find out you put too much/too little mortar on, or you didn't squeeze all of the air out of each floor tile when laying it, etc. And don't be shy with the mortar - I both buttered my tiles and slapped down mortar with a 1/4" square trowel.
Tile edging - Don't make the mistake I did. Figure out what edges your tile floors will have. For carpeting, it's common to set the tile with a metal liner/edge to help protect it from chipping. One side of my kitchen borders a carpeted room, but I didn't think of buying an edge protector before I was laying the tile. It's held up well so far, but I would definitely have wanted to install an edging piece it if had the opportunity all over again.
Time, time, time - Maybe you're a faster worker than I am, but for some reason, laying tile seems to take longer than I expect. So don't just give yourself an hour to do the work before you have to rush off to the shower to get ready for a big night on the town with special tickets.