Screen lanais can get pretty wet and they do get VERY dirty. I don't know why, but our outdoors is always needing to be cleaned.
I love to look at pictures of just what you are looking for. Do not overlook the furniture sold at Home Depot and Lowes, although this is the end of season for a lot of it. And also true of Walmart. They have enormous buying power to get good things and good prices.
Anyway, I love when people are going to decorate. Hope you find just the thing. What colors will you use in your home?
Beautiful screened in lanai furniture pictures. - Bing images