Ceramic tiles for the kitchen are the best in my opinion because they do not mind moisture (like hardwood does).
Olympia is the place to go for tiles, but they are also very expensive. Another place with a reasonable selection at better prices is New Canadians Lumber. Also, "
Tile and Stone" is much less expensive, but the place is fucking chaos and completely disorganized. Drives me crazy to go there.
As far as your floor goes.
1. You need to remove the old vinyl flooring
2. Tiles need to be founded on a very solid subfloor. Experience has taught me that ONLY 3/4" tongue and groove plywood is acceptable for that. So if you have weak subfloor, then you need to glue and screw 3/4" TnG plywood down. (Better yet, rip out your old subfloor since adding 3/4" to your existing floor will raise the finished floor elevation by 3/4" plus the thickness of the tile and thinset.
3. Once you put down a proper subfloor, you need to use either mesh with mortar, or better yet,
Schluter decoupling membrane.
4. Always use spacers when laying tile,
or better yet, these.
5. You need to rent a water saw from Home Depot to make your cuts.
If you want to do a proper job, you need to rip out the entire existing floor (unless it's already 3/4" tongue and grove plywood, which I severely doubt.) That means out come the cabinets.
It's a big job, but with a little get up and go, you can do it.
Lastly, the natural stones such as limestone and marble look sexy as hell, but they require a very very solid floor since they are very soft and weak stones. They are doing some great things with porcelain these days and Olympia has a great porcelain selection. Porcelain does not absorb moisture (like natural stones do) and it's cheaper.