Don't use polycarb, it'll crack. I would use 1-3mm ti if you can get it, but stick to Grade 5 if you go thin. I would prefer 10mm HDPE over ~5mm alu, you want a baseplate to have some flex and not permanently deform and aluminium deforms more easily than the others. It's damn near impossible to deform 10mm HDPE significantly in a baseplate role.

As for top panels the same is true although 5-6mm HDPE (if grade 500 or 1000, not sure about 300) will keep most things out. Obviously nipper and a good pointy axe will go through but that's true for materials weighing 3x more, so it's a balance. Perhaps leave weight to beef up depending on your opponent.

In all cases I would recommend making the base as unnecessary structurally as possible, save preventing a box from collapsing diagonally. You want strength to come from chassis bulkheads.