Glass that is thick enough to be safe in the use you intend to put it to is thick enough to be a beast to cut by hand. Once you get up to 4 feet in an animal enclosure situation, I think 1/4" glass should be the minimum considered. I've managed to cut 3/16", but not a long cut. It is possible to cut thicker glass on a wet saw; I've not done it personally, but if I needed to cut 1/4"+ that's what I'd consider. Old aquariums can be a source for thick scrap glass, though they're a challenge to disassemble and as mentioned simply modding them makes more sense (though wouldn't be my first choice for an enclosure).
People make aquariums and boats out of plywood; done right, a plywood enclosure would not warp. It is the 'doing it right' part that is the kicker, and the expense (and the slight risk of developing an epoxy sensitivity before the project is complete). But that's the kicker with any enclosure, DIY or purchased.
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