Ok here we go...
Plexi = acrylic. Plexiglass is a brand of acrylic.
I stock 1.5, 2, 3, 4.5, 6, 10, 12, 15, 20, 25 and 30mm acrylic.
Granted, this is a single player CP but this has a 6mm, 1/4", top and it has zero flex.

For a 2 player CP 10 or 12mm, 1/2", is all you will need in place of the normally used ply or MDF.
Illuminating the inside of a CP is possible but be prepared to use lots of LEDs to get even lighting. Most LEDs have an effective display angle of 90 degrees. To ensure there are no dark spots a 50mm deep CP will need LEDs no more than 50mm apart. The deeper you go the less you have to use BUT you have to remember that all the buttons, joystick and wires will throw shadows that will require extra lighting to fill the dark spots. This can lead to bright spots...
I'm not trying to talk you out of it because it will look cool if you can get it right but don't assume it will be easy.