Sorry for the long post, I got a cold, can't sleep and just killing time...
I've done a lot of reading into doing basements before I did mine. The one thing I noticed is that builders interpret minimum code very loosely, and not for the home owners benefit. It is minimum code to insulate and vapor barrier a few feet below grade. Why not to the bottom? Because NRC tests show that there is no value in insulating below that. That's good for heat loss and moisture control for the floor above the basement, NOT the basement itself. If you turn the basement into a living space, then things change.
First, the minimum code states that the builder has to put a moisture (not vapor) barrier between the concrete and the insulation but leaving the above grade concrete bare (grade to floor joist/header). This is done so that the insulation will breath through the concrete (believe it or not) for vapor build up behind the VB
. Moisture = mold if it doesn't escape. Vapor barrier goes over the insulation and has to be sealed everywhere to be effective. A small hole can allow 1 cup of water per hour to pass through. So far ok...
Now you finish the basement, throwing up 2x4 16 OC, more insulation, and top to bottom VB
. Now you doubled the area that can hold vapor and limited that area in breathing as well as allow, possibly, wet/moist concrete to touch insulation. You know that musty smell in some people's basement that seems to get stronger as you go lower down the wall. The above scenario is one way to that nasty smell.
But believe or not, you have the opportunity to do right the first time and you don't have to break your budget. Just remove the insulation, chances are it's just roll insulation which you can cut up into 16" batts. If it's already batt insulation then just put it off to the side; bottom line is that the insulation can be reused since minimum code states R12. You just have to buy the extra. Add another two strips of tar paper (it's the cheapest; tyvek works as well) below the existing one (noting that the concrete has to be bare from grade and above; but not completely bare below grade as per code). Frame with 2x4 16" OC with plastic gasket under the sole plate going up outside the tar paper if on the basement slab. There should be a small gap between the concrete and studs for air flow. A single top plate is only required since the wall is not load bearing. If your doing a sub floor (aka Dri-Core or Delta), then do that first then frame on top (don't forget to leave a gap in the Dri-Core between concrete wall and subfloor).
Insulate between the studs where the insulation should NOT be pressed up against the concrete. This space allows vapor buildup in the entire wall to escape via the concrete. The only place where extra insulation resides is in between joists/joist headers. Before insulating the joist/header cavities, spray foam any gap/openings (ie. arround pipes, vents, etc.) to stop bugs/pests from making a nice home. Obviously, if you are doing any wiring on these stud walls, it's easier to do it before insulating and has to be done before vapor barrier. All boxes, water pipes, etc. has to be on the warm side of the vapor barrier so cut squares of 6 mil plastic that will go around the boxes on installation (or you can buy the preformed vapor barriers for J-boxes). Once all wiring, etc. is done, vapor barrier with 6 mil plastic from bottom to the very top between the joists and sealed to under the top sub-floor. A bead of sealant on the sole plate and under the joists/top sub-floor then VB
stapled gives a good seal.
Obviously, the above is not the only way but it is the best way with the least amount to spend. Note that if your basement already has moisture problems, weeping tile problems, poor drainage, the above won't solve it or be immune to problems. Like always, consult a professional if your unsure how to fix a moisture problem. Better to do things up front than cause problems down the road that not only can be expensive but be detrimental to you and your family's health.