You can do the same or use insulation rated for basement use since you already have insulation which will not be in the direct contact with a masonry foundation.

Are studs already in place? Best route is to apply XPS to the wall then build stud wall. If you don't need stud wall in some areas because you won't need to run electrical or similar, there are ways to install drywall without studs (built-in furring, tap-cons, etc.). I have tap-conned osb over foam in a basement utility room. Great for hanging tools, conduit, pipes.

Your best option is rigid foam on the exterior under the vinyl.

See this recent thread for some info.

https://www.gardenweb.com/discussions/5640711/insulation-options#n=20

Now that I understand the issue, you could add depth to your studs with ripped 2xs or I've seen people use foam strips to bump out wall depth so you can fit thicker batts in. The foam would give you a thermal break. There's a thread on greenbuildingadvisor.com for this. You do end up doing some blocking for electrical boxes and perimeter conditions.