A lot of things to cover here. First and foremost is to really emphasize what MarkG said and say that there is quite a difference in water resistance of the melamine foil product you get at Home Depot vs. a 80 to 120 weight thermofused melamine you can buy at a specialty lumber yard or a cabinet shop.
Still, even the best 120 weight melamine is not an ideal finish for a Coastal Carpet Python. If you were to use it I would still recommend covering the floor and first few inches of the cage walls with some sort of more durable product. And here I agree with another poster who recommended putting it on before assembly. If you have access to a lot of tools then simply put whatever you use on oversized and then trim it to fit exactly with a router.
In addition to vinyl flooring, FRP, Sintra or other sign boards and high pressure laminate also work well.
I still think melamine is a great choice for these types of situations simply because the upper cage walls and cage exterior are already finished and look pretty good. I also really like the semi-matte finish of black melamine and think snakes look great against it. It is heavy but the pre-finished nature make it well worth it, IMO. And the cost savings are impressive, especially if you can find some free or cheap vinyl flooring. I have never paid for vinyl flooring I used in a reptile cage.
For assembly, my #1 choice is confirmat screws or a knock off of them used along with Roo glue or another melamine specific glue. If you don't care to buy the special bit for confirmat screws then dados & rabbets are a second choice. Tied with that would be Roo glue plus whatever screws you might have lying around, with extra care taking to not split the material.
One other thing about melamine is the precut shelves that are available. You can often build a cage with minimal cutting. These precut shelves are nice because 1) they are usually a high quality, 100 weight melamine, 2) the edges come prefinished with edge tape and done much better than you can do at home & 3) they care CNC cut and are perfectly square and sized exactly the same - the precut plywood panels you have seen locally are probably cut on a panel saw and not nearly as accurate.
Onto plywood...
Plywood is also a great choice but anything flat and smooth enough to be worth using is going to be more expensive than melamine and still require additional finishing. And this finishing would be required for both the interior AND exterior of the cage. But it is lighter, stronger and does look very nice when finished well.
The Envirotex Lite and other bar-top epoxies are nice but expensive and can be fussy to work with. I happen to like it but some keepers who have tried it have ruined cages, likely due to improper mixing. I have bought it at Menards, Ace Hardware and at craft stores. If you only have one cage to seal the craft stores are a good place to buy as they tend to sell partial kits instead of full gallons.
The downfall to these epoxies is the price and the fact they have to be applied quite thick, making them even more expensive as you need more of it per square foot. I can go into choices for sealing plywood more if you decide to go that way.
-----
Currently keeping a small collection of various Gonyosoma. Both G. janseni and G. oxycephala.