Edge-lit LED panel best materials?

What are the best materials to use for this?

These panels are built in the same way as LCD monitors with LED backlight. Well, monitors have a LCD in front of the backlight panel, but you get the idea. Here's a monitor teardown.

The important part is a thick transparent acrylic plate which acts as a light guide via total internal reflection. It is lit through its edges. And... there is a pattern etched on it which breaks the total internal reflection in order to allow the light to get out through the front side. Without this, the light would only get out of the plate through the edges, and that would be useless.

The acrylic plate is the center of a sandwich, with a white reflector on the back, and one or more sheets of diffuser material in front. A LCD monitor will also have polarizers and, of course, a LCD.

All this is not DIY friendly, but you can get the whole kit for free if you find a busted LCD TV or LCD monitor. Thus... try dumpster diving. Get rid of the LCD and polarizer, and keep only the backlight plate and reflector/diffuser films.

My company was a market-leader in LED flat panel lighting, the basic construction was similar to @peufeu's description:

• LED strips on all four edges (metal-core PCB) bonded to the edge aluminium extrusions with thermally-conductive tape.
• Acrylic block with the front face lightly sandblasted, the edges were just left as the basic sawn finish.
• White plastic reflector sheet
• Aluminium backplate, this screwed into the aluminium extrusions and held everything together. The acrylic block was prevented from falling out the front by a small lip on the aluminium extrusions.

The LED drive wires were routed out of the assembly via a small cutout in one of the extrusions, this then went to the driver which was mounted on the back.

Illuminating the edges really is the most effective way of producing a very even light with no spotting. Rear illumination invariably requires heavy diffusing.