Any of the following materials will work well in at least the thickness specified.

XPS up to 2ins.; EPS 4 ins.; closed cell spray polystyrene of 3 Ins.; open cell spray polystyrene, 10 ins.

No vapour barrier needed. (Unless a clueless municipal inspector still insists on it.)

If you can slip sheets of XPS between the framing and the foundation walls, do so. Even if it's just 1/2" sheets, it will be very effective in reducing moisture.

Here is a link that might be useful: Building Science Corp. on Basements

Thanks. Should I try to seal around the XPS? Or just put it in the cavity against the concrete?

Any thoughts on the most economical rigid insulation? What about the best way to install, considering the drywall is gone four feet from the bottom?

Bert

As long as the boards are tight to the wall, there's no need to seal.

EPS is the cheapest satisfactory insulation. But it robs space because of its thickness. The most important part of the basement to insulate is the top of the wall, especially the portion that is abovegrade. If you're trying to keep the drywall, I'd try to push up enough EPS so that it tightly fills the space. Not ideal. But it could be effective.

Does it matter if the exterior basement wall has a covered porch or garage (on a slab with dirt fill) on the other side?

I have an insulation company as part of a weatherization program here today, and they said that this situation is like a 'party wall' and doesn't need insulation since it's not an exterior wall.

Does that make sense?

By the way, none of these wall in question are above grade.