I would like to put drywall up on my basement walls, my home was built in 1942. It has cinderblock walls. I did major repair on them, filling gaps and cracks. I have covered them with waterproof paint, I had seepage from the ground level so I had an internal drainage system installed around the perimeter to eliminate this. The company that installed it suggested that I not attach the 2x4 framing to the wall with nails to avoid creating any "holes" for water to find it's way into. What type of adhesive would I use to attach the framing? Should I put the rigid foam insulation up first then the framing over it? Never tacked a project like this before. Can I have some suggestions please?

Most framers would make a bottom plate of PT lumber, a standard 16 or 24" wall with a top plate, glue the lower plate and /or anchors and nail the top plate to the ceiling joists. Nail rigid foam to the rear side as a vapor barrier and use regular fiberglass in the stud spaces. Space off the wall by 2". Block walls are too porous for nailing to.

Using metal studding would not require exact cutting. This will make installing S/R easier also.

If you have a moisture problem it would be best not to use fiberglass insulation. It will hold moisture and create mold.

Chuck

This Old House has a good way (but of course it's expensive).
Do above suggestion but use Great Stuff foam behind each stud. The theory I think is that rigid foam won't conform exactly. I took 45 year old walls out of a basement and a gazillion flat bugs scurried away. They live between the wood and the concrete as long as there is space. I would not even build walls in a basement built in 1942, no matter what you had done to it, for at least a year, while you observe it's ability to stay dry, and do a moisture test with a square of plastic.
Waterproof paint doesn't last long. Hydrostatic pressure is too great.
Drainage under doesn't solve all dampness problems.
Concrete is porous!