* Get some plexiglass laser-cut
I am assuming Cherry MX switches here.
1.5 mm plexiglass is too brittle to be used on its own - it would need a PCB.
Thicker plexiglass means that the switches will not snap to the plate, so you would need to glue them (or use a PCB).
However you could cut three layers of 1.5 mm plexi and glue those together with superglue, with the top layer made for the switches to be snapped into - that should be strong enough but not transparent.
Yet another option would be to make a PCB and use PCB-mounted switches. A few guys have made PCBs at home with kits from a store, but it is easier to reused a part of a PCB from an existing keyboard with PCB-mounted switches, reuse part of the matrix and hand-wire the rest.
* Sytrene structural shapes (from a hobby store) assembled into a frame for the switches
That would involve a bit of cutting... and styrene can not be laser-cut.
I think that pure Polystyrene (PS) is actually too brittle, but HiPS (polystyrene with butadiene in it) or ABS (HiPS with acrylene in it) would work well. Often styrene is only labeled "styrene" when it can be either type of plastic.
Another question, is there a certain type/gauge of cable I need to use?
Not really. You could cut up a ribbon cable into individual cables, and have it remain connected near the controller - that could be more tidy than a rats-nest of wires, but requires more thinking ahead.
I must warn you that programming the firmware is not straightforward. Most freely available firmwares for the Teensy 2.0 are made for regular keyboards, with sometimes media keys as an add-on.
The key codes for media keys are in the "Consumer" Usage Page (0x0C) in the USB HID standard.
I have assembled the codes in
a table on the Deskthority Wiki.
