[Tristan Lall]

Stay away from Plexiglas (acrylic), because it cracks easily. Lexan (polycarbonate) is much more durable when used on robots, and it's easier to work with (less melting when being machined). The thickness depends on what you want to do with it, and how well it's supported. Metal or heavy plastic (e.g. HDPE) are certainly valid options, but by no means necessary.

Consider that you may want to make your electrical board a structural component of the robot, adding stiffness and reducing the need for other structures.