By "half walls" I am assuming you mean some one has furred out the walls with 2" strips so that the wall is 2" thick.
Whatever you choose get rid of the plastic. It is a mold issue waiting to happen.
Around here code requires that finished basements be studded in the normal fashion and insulated with R-13 (3.5"). The cost to add another 2" will almost equal the cost of buying studs unless you rip your own 2 x 2's. Polystyrene can be a serious hazard in the event of a fire. Better check your local codes for it legality in your area. I would rip it out and stud it up if I were going to live there or replace the plastic with something that can breathe and finish the walls as they are. R6 vs. R13. What is the cost of heat or cool where you live?
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