Screw type for screwing MDF onto plaster/plasterboard
Given: 


  The existing wall is plasterboard and plaster (fair condition at best)


I would lean heavily in the direction of stripping to the studs and then attaching the MDF to the studs, but that's making the assumption that the MDF is of some reasonable thickness (12mm / 1/2 inch or more.)

Fix anything that needs fixing in the wall cavities while you are at it (insulation, wiring, plumbing, etc.)

Sheeting over poor-quality plaster/drywall reveals in great detail exactly how non-flat the substrate is, and eats space in the room. Despite the brief mess, starting fresh may be faster overall (as you are not compensating for all those humps and hollows), and result in a better job.