In reply to Martin Davies:
Are you sure it's concrete? That'd be a fairly unusual material to have above a door except as a lintel. If it's a lintel I'd avoid drilling/screwing into it, there'll be re-bar in there which you don't want to hit/compromise/expose.
Why not screw the finger board straight to the wall?
Simple answer to your question: Plywood, 18mm, simple and hard to get wrong.
I'd put wallplugs in and fix it direct.
jk