If you have a professional in to do a moisture test, then you will have a better idea of what you are dealing with and what is going to be appropriate. Just off hand I would say you will most likely end up with an engineered wood if you are thinking wood, in a hardwood like oak with a moisture barrier. The backside of your flooring should not be accumlating moisture as it is not well sealed. The moisture barrier may collect some moisture, but it also doesn't absorb it and lets it evaporate.

Also be sure to double check on materials and proper application so you choose appropriately to minimize the chance of any issues. Not all materials can go on grade/slab. Worst case scenario you could do a stained concrete or poured epoxy floor with area rugs.

Good luck!