Put your vapor barrier on the warm/heated/interior side of your stud wall (just like upstairs). The paper face should be enough of a vapor barrier in a basement (even in NJ or points north) although some may say to go for the overkill and place the plastic right over the paper face but I wouldn't do it that way. If you want a plastic vapor barrier (since its vapor resistance is better than kraft paper), then use unfaced insulation so moisture doesn't get trapped between the two or cut slits in the paper to avoid moisture trapping.
Plastic is usually only put directly on a basement concrete/block wall as a "moisture" (not vapor) barrier if you have moisture coming through the basement wall from the outside. Then you probably wouldn't want a vapor barrier. Get a humidity guage and be prepared to run the air conditioner (which is also a dehumidifier) to get rid of moisture during the summer. If you are really concerned about air quality, then you may need a dehumidifier in the winter (since you don't want to run the a/c) or also consider a fresh air/ventilator setup. Good luck.
Just wondering if you are using wood or metal studs and why you made the choice? Also leave a 1/2" or so gap between the stud wall and the basement wall for an air gap so the insulation and studs won't contact it and possibly wick moisture from it.