Pretty much anything that can be grown in the ground in zone 9 should do fine in that area. My lanai has a roof, it doesn't get nearly that much sun. I use it for a recovery area for fresh repots. One thing to keep in mind, pests somehow manage to get in the enclosed areas but their natural predators do not.
If you decide to get tropicals you will need to give them some protection when it gets below 40f.