It helps to know your zone, but without knowing your state these trees might not be available in your area.* I might recommend different trees and/or shrubs if you are in zone 8 in Georgia then if you are in zone 8 in Arizona.* What state are you in?
When you say shade, how much sun per day does the area get.* Shade would be 2 hours or less of sun.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.