I personally don't see the problem with the "weird sandwich". The tiny bit of insulation the builder put there (likely because they had to meet local building codes) doesn't have a high enough R-value to do much for you on it's own, but I also don't see why you would tear it off when you could just add to it with more between the studs.
Like @Nemo said, in my basement and anywhere else I've seen in Canada, you just frame your wall with a small air gap to the crappy "builder" layer of insulation, put in your own batt insulation between the studs (with an appropriate R-value), then vapor barrier and drywall. It's really an easy way to do it, you know you have good insulation, and you're only losing a few inches off the whole space.
I've seen a few ways to deal with the floor / sill plate, but I just used the blue/green "treated" 2x4's for the base of the wall. I also used a product called DMX 1-step on the floor that comes in a big roll, and gives an air space under your floor to reduce the cold coming through, and in case you get any water.
Also as others have suggested it's a good idea to insulate (at least with something like Roxul Safe N Sound) in the ceiling so you don't get a cold pocket, and it also helps with noise transmission. When it comes to things like insulation in a basement, I'd tend towards overkill versus saving a few bucks. Depending how big the space is, it's only going to cost a few hundred to insulate really well yourself, and once you drywall and finish it you're not going to want to tear it back open again. Do it well once and don't worry about it again.