[ Ref. Joe Slaven in 211128 MMDigest]

Hi, MDF would be unsuitable as a material as it is acoustically dead.
Robbie gives very sensible advice below your message. Victorian musical
boxes always had softwood soundboard bases, even if the rest of the
case may have been a hardwood.

I'd suggest it should be thick enough to be able to secure the movement
to it, but apart from that it is probably not very critical.

Hope it turns out well!

David Evans - Editor, "Mechanical Music World,"
Journal of the Association of Musical Box Collectors
https://www.ambc.org.uk/