Insulating and framing a basement after drain system and plastic vapor barrier installed
You can do almost anything since it should be fairly dry on the inside side of the vapor barrier.  Best would be some kind of material that can tolerate a little water and resists the flow of vapor.  Any humidity in the basement air will tend to cool when it touches the vapor barrier and condense into water on the wrong side of the vapor barrier.  

Sheet XPS or PolyISO Foam with seams taped would work and be an easy DIY project.  

Better would closed cell spray foam installed by a contractor. 

For a lower budget option you could go with a mineral batt insulation that is vapor open but will tolerate being wet without being a food source for mold.  

Fiberglass batts are probably the worst choice since they tend to degrade in moist areas.  I would not recommend them.

Do not put an additional vapor barrier on the inside side of the wall, this will just trap moisture inside the wall cavity.