Our local home improvement store sells unfinished wood screen doors for $35. Once you said "rot", I think new is the way to go.

I love recycling and if this is old it’s better wood than the new ones. That said you need to buy a heat gun to strip the paint. For the rot look at abatron wood epoxy- it soaks into the wood and hardens it. Too much work for a screen door but it’s a great project to practice on because it’s just a screen door.

Thanks @AnnKH and @HALLETT & Co. The problem with buying a new door is size - this is a custom size unavailable in stores. I'll look into a heat gun. Appreciate it!