Insulation, Radiant and Vapor Barriers - Help! Basement Insulating/Moisture/Vapor Barrier

Hi. I am finishing my basement and have been trying to figure out how to insulate the basement 1/2 wall (concrete) which probably only about 2' of it is below grade.

The wall above the 1/2 wall is already insulated with faced batt. I framed a full wall about 1/2" away from the concrete wall. I am now confused as to what I should do to insulate the 1/2 wall (concrete). I've read about extruded polystyrene as the best approach but they seem quite pricey especially since I already have a lot of faced batt available that were used on the basement ceiling. I figured I would not need that anymore since the basement will be heated once finished.
I have read about using 6 mil polyethylene on the concrete wall. Can I then use the faced batt over the polyethylene? So that would be concrete wall - 6 mil polyethylene - faced batt - then drywall.

Finally, what do I do with the empty space above the 1/2 concrete wall between MY framed wall and the original wall.

I hope I am making sense here. I'll appreciate any help!
BTW I am in the Northeast.

Polystyrene IS your best bet, it is (from my experience) the most efficent option available to you, and if you go that route you will not need to use polyethylene. However it is the most expensive of your options considering you have loose batts laying around. Your best bet would be to use those batts for your halfwall. You will want to put the polyethylene on after you put the batt in the wall, (Concrete wall, batt, poly, drywall) You always want the poly on the warm side of the insulation. Having said that you may... have different building codes that i do in canada. Maybe you are thinking of tyvek? Tyvek would wrap the outside of the concrete.
As for the space above you concrete wall, i would frame it to the original wall, then stuff scraps in there, then poly, and drywall. Hope this helps a liitle for you yersole.

I've been researching this also, and have a few comments.

If you have faced batting, then the facing is (probably) already a vapor barrier. And you don't want more than one vapor barrier, or you will trap moisture in between the layers.

You need to insulate the wall, the put the vapor barrier over that. I think may foams act as vapor barriers as well, so depending on what you use, you may not need the plastic.

Anway, you definitely want the vapor barrier on the warm side of your walls. So in your part of the country, you want the vapor barrier to the inside. In the deep south, you would want the vapor barrier on the outiside of the insulation.

Thanks guys for your input. After more research it has come to my conclusion that extruded polystyrene might just be the best bet to put up against the 1/2 concrete wall which part of it is below grade. I've read that I can then stuff unfaced batt (is that simply removing the paper from it?) between the polystyrene and drywall.

Now what I am still confused about is that my 1/2 concrete wall will be insulated as stated above. What then should I do with the space above the 1/2 wall between my full wall and the original wall above the concrete 1/2 wall (which btw is using faced batt). There is a good 5-6 inches of space.

You do want the V/B paper to the room side there. Most of the time we make that off set to the other outside wall a step like that you can use as a book shelf . All around the room