Replacing vinyl with tile

I am looking at undertaking a "major" project at home where I'll be pulling up all the vinyl in bathrooms and laundry room and replacing with tile. A portion of the subfloor is concrete (lower level) and 1/2 or 3/4 plywood (top floor). What is the best way to tackle the removal, prep and replacment with tile?
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wrote:

Ceramic tile or what?
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On concrete floors, with well bonded vinyl, I have used a 2 part thinset made by mapei. No need to remove the vinyl. This made the high cost of this special thinset very attractive. I have done a few jobs like this over the years and all have held up with no problems. Check with you local tile supplier to see if it can be used on plywood floors.

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