polycarb plates (usually half plates) are popular. polycarb is softer and much more pliable than acrylic. some have machined cases from large blocks of polycarbonate.
acrylic (perspex) is probably the most popular stacked/layered style case.
- check out qlavier for inspiration, they do beautiful layered cases
FR4 make good plates and most are semi transparent (will diffuse light) depending on the finishing of the top & bottom surfaces
- you can do a really cheap spaced FR4 case. FR4 plate, pcb, FR4 bottom plate all held together with standoffs
another option would be to 3d print. or even better, 3d resin print
as far as vendors... check
http://builder.swillkb.com/ https://lasergist.com/ (stainless steel)
https://www.ponoko.com/ (all kinds of materials)
see what other vendors are suggested, these are the couple that i know of, may depend on your location as well.