What may I ask are you needing the Melamine for? you can just use the normal plywood, just use a good stain to seal the inside of the wood and you'll be fine. The cage doesn't need to be waterproof since you're putting a beardie in it.
As for your glass, it all depends on what you want your cage to look like. I would wait till you have your wood all put together. If you're using the Stanley track like I did, then it will tell you how to come up with size glass you should cut..leaves just enough room to slide into the top track to get the bottom in, and fit nice.

On the front of my cage, the glass acually goes behind those front side pieces of wood on my tank. Gave it a nice sleek look.

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