Cork board is terribly soft, sucks up paint like a sponge but has a fantastic rough surface to adhere to.
I do not like how it has a fair bit of spring to it, which makes rolling dice on it "exciting".
I find it is also an insanely expensive building material.
Foam can be almost any grade you want, I was awestruck when I got to see custom foundry pattern foam that you can machine (yes, milling machine):
https://www.generalplastics.com/markets/tooling-and-molds
This stuff becomes more of a challenge on how to cut it.
For insulation, you should look at the technical papers and see how "hard" a foam you prefer to work with.
You would look for "Compressive strength" like what I found for Foamular sheet:
C-300 = 30psi
400 = 40psi
600 = 60psi
1000 = 100psi
(Just love product names that match their properties...).
Usually the surface hardness is not as important since I tend to hit it with a few coats of watered down white glue for a hard surface.
I think it really depends on what kind of use the terrain may see.
Flat surfaces you can add another layer of laminate or plasticard / styrene something to give some impact resistance say if it is heavily used
FLGS terrain.
I found it handy for gluing/welding plastic detailing directly to it for extra durability.
I use combinations of steak-knives, hot wire cutters and an electric carving knife for cutting this stuff.
Scroll saws would be ideal but I have not got into those yet.