If you use plywood, just buy WBP grade. 12mm is fine, you can get away with thinner, but if you have the depth use 12mm.
The experts will say use tile backer or cement board as previously mentioned, but plywood is fine. I have used both, the cemnet board is more expensive, but allows you to use a higher wattage underfloor heating matt if required.
Check the specs on the adhesive you use for recommended fixings spacing. For 6mm ply it can be as close as 150mm centres but for 12mm wbp, I usually nail (rinshanks) or screw at 300mm. I assume your existing floor is chipboard or T&G ?