You can put a vapor/moisture barrier up over rigid foam. A lot of new construction in the far north has this as a default. The idea is that you frame right outside of that. In that framing you are allotting a cavity to which moisture can move and evaporate.
Now if you are putting rockwool or other types of insulation in your framing then no you do not use a moisture barrier. This would in essence trap water which will condensate on the plastic and promote mold growth on drywall. I am not that smart this is just doing a lot of basements and reading the Building Science reports that are out there for the past 5-6 years.
Ask yourself this: "If I install a vapor barrier, where is the water that it stops going to collect?"
If you put a polyethylene vapor barrier behind a drywall-covered stud framed wall, then the answer is that water that condenses on the poly will fall onto the wood sill plate, growing mold and eventually rotting it out.
Dedicated vapor barriers have no place in a basement wall. If the basement wall is insulated on the outside, then the vapor barrier is superfluous; otherwise, is it dangerous, as it will trap moisture against a moisture-sensitive element, as I indicated.
Here's lots of supporting evidence, since this perspective appears to be controversial. From http://www.greenbuildingadvisor.com/blogs/dept/musings/how-insulate-basement-wall
Should I include a polyethylene vapor barrier?
No. Basement wall systems should never include any polyethylene. You don’t want poly between the concrete and the insulation; nor do you want poly between gypsum drywall and the insulation. You don’t want poly anywhere.
Paul Ellringer, an energy and mold consultant in Saint Paul, Minnesota, has a collection of slides showing moldy basement insulation. In most cases, these basement walls were insulated with fiberglass batts, and included two layers of polyethylene — one on each side of the studs. Ellringer calls this a “diaper wall,” and reports that most of them are a mess. “Fibrous insulation and poly are inherently problematic, and should not be used in below-grade walls,” says Ellringer. “Sometimes when you open it up, the fiberglass is soaking wet. If the house is two to four years old, the studs are often beginning to rot.”
And from http://www.buildingscience.com/documents/information-sheets/basement-insulation:
No interior vapor barriers should be installed in order to permit inward drying.
And from http://www.buildingscience.com/documents/digests/bsd-103-understanding-basements/:
Unfortunately, locating insulation layers on the interior often conflicts with the traditional approach of foundation water control – namely inward drying. Constructing frame walls, insulating the resulting cavity and covering with an interior plastic vapor barrier is common (Photograph 2) and often leads to odor, mold, decay and corrosion problems (Fugler, 2002; Ellringer, 2002). Also common, and prone to similar problems, is the use of “blanket insulation” often derisively referred to as “the diaper” for the odor problems associated with the approach (Photograph 3).
If you have not yet constructed your stud wall against the existing basement wall, please read those links to find out how to do it safely and properly.
Best Answer
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.