If you look at a lot of the designs for a retrocade online you're going to see a lot of MDF being cut and formed. This is because MDF is very heavy and anything built out of it will be very stable.
STABILITY IS IMPORTANT!
When you play one of these machines, your whole body tends to interact with it. As you twist and turn (needlessly but God it's fun!) playing the game, the cabinet has to absorb and anchor all those changes in force. Also, back in the day the cabinets would have quite a bit of money in them and the added weight was a security bonus.
MDF is heavy which means it's a pain to work with. It's also really tough on your blades as well. Then there's the kind of sawdust it kicks off, which I find toxic. I use MDF when it's necessary (which is a lot) but I really don't think it's necessary here. Plus I want to be able to pick this thing up from HQ and walk it down to the shop for modifications and paint without calling in a buddy.
My solution is to build a lightweight frame to support all the necessary components. Then once I'm happy with this frame+bolt-ons (a chassis), I'll use cheap, LIGHT, 1/4" laminate (theatre geeks know it as Luaun) to make it a look pretty.
If all that sounds familiar it's because it's the exact same way you build cars and theatre sets.