I am tiling mine so no issues regarding final finish and plywood will
be sufficient. If you want a paintable top notch finish I would
probably use plaster board instead of plywood and then skim this.
Basically you would be constructig a stud wall. I wouldn't skim the
plywood unless it was thick as it would probably be too flexible
resulting in the plaster cracking and falling off (?) Also I dont thnk
you would get the finish you are after by just sanding the wood and
painting.

Someone else may come along with a better idea though........

Cheers

Richard