Grumpy - if it was me and I was going to tile over it I would have left the vinyl alone for 2 reasons
1) Asbestos. The norm is to cover not remove according to EPA.
2) You are going to cover it with backer board anyways, as long as it is not more than 1/8 out of level due to missing pieces or such it is work that doesn't need to be done.
The only reason I would have removed it would be if I had to replace any of the subfloor itself due to spongyness.
In any regard you do not need to remove the white paper.
As far as tiling under the cabinets themselves I would not do that. But I would tile under the dishwasher, the refrig and stove.
- Dishwasher - so it can be easily slid out, trying to get it over the tile lip later if it has to be replaced may mean having to remove the counter!
- Refrig - you would have to tile at least 6 inches under the front of it anyways or you would see the subfloor under the front, then you would have to shim the back to level it, so just tile under whole space under the frig.
- Stove, is the same as the fridge so just tile under the whole thing.
The other thing is if you are going to do anything really nice like a different tile boarder that traces the perimeter of the floor and then set the field diagonally, it would be a lot harder to try to measure out from the wall to where the edge of all the cabinets would be. Lot more work than just installing the cabinets and then tiling the floor that is left. Besides, why waste the money on the extra tile. (Put the kick plates in before the tile so you get a easy and seemless look, leave a groutlines thickness between the tile and the kick plate, caulk this seem with matched the matching colored caulking that you can get in the tile dept, this is where water will get under the tile from splashes at the sink)
To tile it you need to put down 1/4 inch thick cement board. (no vapor barriers, tiling a shower stall is a different story) Coat the floor with thinset morter. There are 3 thinsets (not counting colors) the cheapest is just thinset and water, the middle is thinset and you add acrylic latex additive instead of water, the third and best is thinset with the acrylic latex additive already in it and you just add water. I would use the last one. It is the best of the three and allows the most flex, giving you the best chance at not having grout lines pop down the road. It is also the most expensive, but I would never use the first one, and the second one means you always end up with either almost a full bag of thinset left over and a little bit of the additive, or almost a full bottle of the additive left over and a little bit of the thinset left over, you can't win unless you are tiling all the time. The last one is more expensive, but it could actually end up being cheaper. Screw down the cement board with the special screws made for it according to the screw pattern recommended.
This floor prep will give you the base you need for a trouble free installation and a long lasting professional looking tile floor.
Some things to keep in mind
- Cut all the cement board first, laying them in place without attaching, then remove them all and then apply thinset and screw down all at once. One piece at a time is a pain in the butt.
- Since your cabinets will already be in place, I would leave the doors off still. Be very careful getting the cement board in place, slide it up to the cabinets instead of dropping it to the floor, one scrape of that stuff and your cabinets are gouged.
- Don't scrimp on the quality or the look of the tile you want, it is a major pain to replace. Stretch the budget if you need to because you don't want to do it twice.
- Thinner grout lines will stay cleaner and look nicer in the long run. Keeping a tile floor clean is not about the tile, it is about the grout lines.
- Go with the darkest grout lines you can stand - see above.
- Seal that grout!!!!
If you need help with how to start the layout of the tile just holler.
