Foam board insulation is easy to use and is a great diy way to add some insulation.
Tile over foam insulation.
You can use either one or two layers of plywood or osb and the subflooring can either be fastened to the concrete with long tapcon screws or it can simply float above the foam.
No neither ceramic tile nor wood flooring should be installed directly over rigid foam insulation.
It comes in standard size 4 8 sheets and smaller sizes in many different thicknesses from 1 4 inch to 2 inches.
Both require an isolation board or slip sheet.
If anything i would use 3 4 exterior plywood over the styrofoam and then an isolation membrane and tile over that.
If your basement slab lacks sub slab foam you ll have to install the insulation above the slab.
Some types of thicker foam board insulation are available but they may need to be special ordered.
There are several ways to install subflooring above the rigid foam.
12 pk blue charcoal acoustic foam tiles soundproofing foam panels sound insulation soundproof foam padding sound dampening studio sound proof padding 1 x 12 x 12 4 2 out of 5 stars 501 19 99 19.
I usually stick them down with ardex x7r or mapei keraquick lay the ufh slc with arditex na or mapei fibreplan then tile with x7r or keraquick subject to the type of tiles being fixed.
2x2 foot foam tiles are easy to install over concrete tile or any hard flat surface for basement floors kids room and home exercise areas.