1/2 concrete backerboard (or DuroRock) would be my first choice.
1/4 Hardibacker board would be my second choice.
Remember height is a consideration in your selection. You may have to cut doors and install reducing thresholds where the ceramic tile meets the carpet, vinyl, wood, etc.
Use lots of screws and liquid nails to secure them to the plywood. Your floor should not buckle or move when you walk on it.
Wire lathe on felt paper would be my third choice. This would be nailed down.
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