Size sounds great. Aluminum window screen, either bright aluminum or charcoal coated, is fine. Fiberglass screen is fine too, just softer and easier to damage. What you want to avoid is galvanized mesh, like some chicken wire or landscaping mesh. The galvanizing is very rough and can irritate or cut the feet. Some chameleons will climb the screen and they can get a nail caught and torn out, but I think if you have enough branches and vines, you can minimize that risk.
Building an enclosure is so much fun. Under the Enclosure sub forum, there are two sticky posts where people share their enclosures. There are some great ideas there. The first link is the post that I based my custom enclosure one, mine is the second:
https://www.chameleonforums.com/diy-chameleon-mansion-build-102657/
https://www.chameleonforums.com/thank-goodness-9-ft-ceilings-111618/
There have been at least two beautiful armoir conversions on the forum in the last two months, too.
Don't be married to the 24x24 size at first - figure out how you are going to handle water drainage, then base your cage size around that. If I were to rebuild my cage, I think I would do it around some sort of prefabricated drain - like a sink base or shower pan.
I agree that it definitely won't be cheaper than something you can buy, but honestly with a lot of care and planning, it's not too hard either. I did it without any power tools, just a lot of patience and elbow grease.
Welcome to the forum! Post photos of your new cage! I always love to see what people make.