I just painted my first coop and didn't go with a heavy duty type. First of all, I wanted to use a warm colour and marine paint, etc. that isn't white, is hard to find and second of all you need to give it a few weeks to air out before you put chickens in it. So I went with a very low odour, fast drying exterior paint that I can wash (but not scrub hard) with a disinfectant solution when necessary. I also use so much pine shavings that my coop floors don't need a hard scrub.
I feel confident that the plywood sides and floor have a reasonably good seal on them and as long as water doesn't sit on the paint but runs off with it being exterior, it'll be fine when needing a wash.