When I had my roof leak repair, the roofing contractor also suggest to remodel the siding of our house. We went for backed foam which is sturdy and not likely to warp.
Bella

Here is a link that might be useful: roof leak repair

from an efficiency pov
put the foam board on the exerior of the walls.
tape all seams.
put regular vinyl on top.

little strips of foam board do little
to stop air movement as foam is not continous.
using foam sheathing on walls before cladding
is by far the better install.

we have a home improvement company locally
that sells 'insulated' vinyl. they overcharge
so much that they offer a 'free' 4 wheeler.
kinda lets you know that they are making a ton
of extra money.

I've heard of folks that bought into the scam
and paid 20K for a 9K job.
its sad.

put the foam where it works.
vinyl siding moves
insulation shouldn't.

best of luck.

I researched the foam backed siding extensively. My conclusion was that while it may be sturdier than plain vinyl, its efficacy as an insulator is dubious. Without lapped or taped seams air will infiltrate and compromise the insulation. You also have to be careful about moisture management. Some foam backed vinyl has ridges and channels to drain water, but many do not.

I chose instead to sheath my house with Zipsystem r6 insulated panels which are taped at the seams and have an integrated water and air barrier. On top of that we're installing a 3d polymer rainscreen and fiber cement siding. No housewrap required.