Any paints can be used. If they have fumes, just let them air out well prior to letting the chickens in.
Certainly I'd pick a good water based paint, because they are easy clean up, and very good quality these days.
Sort of an exterior plywood, which is very sturdy!
I'd consider swapping out the chicken wire on the window for 1/2" hardware cloth. Some predators like raccoons can rip through chicken wire.
I like the double doors that open for cleaning out.
Will your chickens free range during the day...
Good point.
Your 4 chickens will spend as much time as they can outside of the coop, and only use it to sleep in, or to lay eggs.
If you add a decent sized secure run with a roof (plastic patio roofing is fine), they'll be out there, or free ranging if they are permitted.
You can even make the...
This could work well for a couple of years until you figure out what you want longer term.
If this coop will be installed inside of a larger run for bad weather, or when you are gone, but then they'll free range in your back yard when possible, then I think it should work!