I would tear everything out, check that the bare concrete is level, so you can live with any minor slopes, otherwise, level it with self-leveling compound or similar.
Then primer, adhesive, tiles, and grout. The manufacturer probably has good instructions for this. Don't forget gloves when grouting.
The bare concrete so you don't build in anything that could cause mold/problems later. The grout lines will also "breathe" moisture.
Your big problem later will be that you get cold floors since these tiles will be cold. Installing a thin electric heating underneath will probably be a relatively expensive heat source, especially if you have hydronic heating with some type of heat pump. Running hydronic heating is a completely different thing, search for basement projects.
If you can live with wearing slippers or aren't very sensitive to cold, you'll have a good basement floor that's easy to keep clean.