With money anything is possible. Proper insulation of the room's "envelope" plus good exterior waterproofing and grading can result in living space. Whether the expenditure is worth it only you can decide.

If we were to build on top of it, because we expand the main floor, will that structure act as insulation for the ceiling?

If I'm understanding T.J.'s question, it's the same as ours.

What methods and materials will best insulate this from the adjoining living area, without causing any moisture issues in either one?

We are in Minnesota, and have this exact same thing. We have asked different contractors for advice, but there doesn't seem to be an exact answer.

We do not want to make it a living space (although the water main comes through it, and the water softener has to be in that area.)

Our current plan is to line the interior facing wall, ceiling and the top 2' of the exterior facing wall with 2" EPS foam, sealed at the seams with spray foam. But we are still researching this idea...

This issue is best addressed by a licensed "environmental engineer". The "how" depends on many factors...the type of existing "floor" (dirt, gravel, concrete and how thick it is...and does it have a vapor barrier?) is only one of many questions. Every situation is different. I can tell you that specialized rigid foam boards applied to the exterior walls and spray foam applied to the interior is the best form of insulation.

Our floor is concrete. What type of vapor barrier is needed? Between the concrete and the foam?