If you going to use mdf don't let it get wet as water and mdf don't mix.
Avoid acrylic sheet as it can be a bit brittle and crack under heavy impacts and can be affected by most solvents. Polycarbonate sheet could be a good choice but my favourite would have to be carbon fibre sheet with a fibreglass core, strong, light & a bit flexible only one real downside it does tend to be rather expensive unless you can find someone that has some with imperfections in that they are willing to sell cheaper.