The roof of your coop should be made out of thick plastic (1cm thick) and tilted at an angle of 46 degrees This will make the water flow down when raining and you can place guttering on the roof leading down to a bucket or something, creating a water supply for the chickens. Regarding the welded mesh, have the opening size about 1cm wide, and if you have a snake problem, slightly less.
I'd suggest either a metal roof or a standard shingled type roof (or if on a budget, wood with some sort of waterproofing on it can work but may not hold up as long.) I haven't seen plastic that'd be thick enough for me to want to use as a coop roof, I'm sure it exists but it's not the type that's sold at our usual big box stores. There's pros and cons to roof choices just as with anything else. My roof is metal, which is a pretty popular choice and is fairly strong, but it can have condensation issues depending on climate, amount of ventilation, and installation. I have plywood sheathing under it to prevent any possible condensation from dripping.
1 cm mesh openings would certainly keep out almost every small pest I can think of.