What thickness should each piece be if I am making a sandwich style case?
They can be as thin or as thick as you like!
The only true restrictions are:
1) If you want the plate to be one of the sandwich layers, that layer needs to be proper plate thickness (1/16", iirc)
2) The total room inside the case needs to be enough for what you want to put inside it (obviously).
A basic sandwich case only has three layers -- one for the plate, one for a "spacer" layer of whatever thickness you want (within reason), and one for a bottom layer. You can split up your spacer layer into multiple thinner layers for the same overall thickness, or you can add multiple spacer layers to make a thick keyboard. You can also add a layer or layers above the plate, forming a raised bezel.