First, as you say, remove the particle board and vinyl first. After that, you need to have at least a 3/4" sub-floor.
On top of that, 1/2" cement backer board, or better yet, 1/2" hardy backer board. The first is best but the latter is lighter and can be cut w/a utility knife.
You may also want to ask the tile mfgr. too what to use because if you use the wrong material, morter and grout included, you could void the warranty. My best to ya and hope this helps.
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