id stick with the floor covered but wouldnt use mdf,far too dense and heavy
ive got ply in mine covered with leather material
had no floor in mine at one point and all you could hear was the pumps buzzing away and stones hittin off the inner arches/sills etc,theres still a bit of incar noise but nothing like it was,id only strip it bare if it was a track car mate

this is how mine looks,albeit not im my car
i use the small square bit thats cut out for some tools i carry for emergencies
and the back comes out to let you into the spare wheel well incase your carrying anything ie jump leads