I'm thinking the amount of sun you get would depend on the type of screening. I live in the South, and I've lived at a house with a large screened in porch which faced South. I had enough bright light to be able to grow a variety of plants. If you don't have much light, you can always do houseplants. Most can tolerate indirect light, and a lot shade.
With a porch that faces West, I can't help but think you would get some direct sun. Hot and humid is ok for many plants. What kind of plants did you have in mind? That determines what to put out there.