I discovered that two acrylic sheets around 300 x 600mm is enough to cut out all parts in the case: Frame, lid and hinges, bottom piece, keyboard switch plate and keys. This size also fits nicely into the laser cutter's operating area
The original plan was to make the case out of wood, but for a prototype, cheaper (and quicker) acrylic would do fine. Of course, I'll have to get the laser cutter working first