Plywood over rigid foam over concrete: will I have moisture issues?
If you have water problems in your basement, look to the exterior of the house for solutions.  Mainly, get water to flow away from or around the foundation.  If water is building pressure behind the concrete, it's only a matter of time before it finds a way in.  In a high-precipitation area, painting the inside of the basement is unlikely to stop the water for long.  If the sealing fails, then you have water trapped behind the foam and that's going to lead to other (smelly) problems.  Previous owners of my home tried to seal the basement from the inside and it simply led to the deterioration of the concrete  at various points.

If you have an old drain-tile setup with actual ceramic drain-tile, get it updated.  The whole strategy of those systems was often inherently flawed.