I’d use tile backer board , light easy to cut and strong plus water resistant and you can tile directly on them.
If I’m screwing them to floorboards I tend to get a thin sheet of hardboard down first then put backer board down screwed down but I use these with the screws, designed for plasterboard but never had a issue
Just be mindful and thoughtful what’s under the floorboards ie pipes , wires etc and if installing new pipes access for these in the future