Kingspan type rigid insulation will not follow the curve of the metal and leave gaps for condensation. Closed cell camping matt is a favourite, or foil backed foam like you can get to go behind radiators.
Be sure to add up all the costs of glue etc…it may not be far off a spray foam kit consisting of two bottles and applicator gun (approx £400) which is super quick and effective.
Don’t use fibreglass style insulation as it will soak up condensation and vapour.
Lino over underlay will probably be quite easy to damage, managed to punch holes in mine and its glued directly to the ply floor.
If you take the bulkhead out, get a heavy curtain to hang in its place, keeps the warmth in the front when driving, and in the back when camping!