Use 1" thk. 4 x 8 sheets of insulation board(not sure of brand name) attach with firring strips, very easy to work with. Better but more expensive and harder to do would be to add a 3.5" stud wall against the concrete blocks, insulate between centers. Cover and finish with drywall if you want. Herbster
If you try to fasten the furring strips to the basement wall with a polyurethane construction adhesive, I would be worried that they would stick to the paint, but not to the block and they would not be secure. I could be wrong, but that would be my concern. I believe that a power actuated concrete hammer (you can buy one at HD for $20) or concrete screws would fasten the furring strips better.
You’re going to have a hard time fastening any covering to the foam itself - it just won’t hold. If you are already sold on using furring strips, cut the foam to fit between the strips. Make good measurements/cuts to avoid gaps. Insulate between the furring and attach your covering (drywall, paneling, whatever) to the furring strips over the insulation.
Might as well use 2x furring and have an extra inch of insulation. little additional cost/hassle but double the insulation.
foam isn’t heavy and will do fine if you construction adhesive it to the wall. but you can’t cover it with this method.
You will also have to add a vapour barrier on the inside or you will end up with mold issues if you cover the insulation with any material.
Adding a plastic vapour barrier will make it virtually impossible to attach anything directly to the surface without using fasteners into studs or strapping.
Insulating the way you want is possible but realistically finishing the inside without having something more solid to attach to is not practical
(and it will probably took like s**t in short order).
invest in one of those nail guns that use the gunpowder charges ($20 at homedepot for the one you hit with a hammer). excellent for driving nails into cement/brick/whatever. worth every penny.
and some of those foam boards - in particular the one with the reflective side - also are a vapor barrier. you’ll have to spray foam the edges to complete the seal.
I’d set a 2x4 flat against the wall every 4 feet. power hammer it to the wall. stick a full sheet of foam core in between with enough liquid nails to hold it. seal the edges with spray foam. attach paneling or whatever. might also add a “stud” in the center of each wall (or wherever people tend to want to hang things) so there will be something there for support. This should not be a complicated job.
shoot, could even run wire for electrical/cable/computer lines under there.