Welcome, Littlelynzi!
The first two things to consider is how much sun the area will be getting, and what soil texture it will be going into. These two factors will affect both the plant palette available, and construction methods.
Also consider the kind and proximity of the tree and bushes. Trees and shrubs with invasive roots are going to cause particular challenges which need to be met. Nearby trees can also inundate the rockery with leaves each fall, and most rockery plants don't like either being buried in leaves, or being raked over.
Others will probably be better at suggesting particular plants for you, because my climate is so drastically different from yours!

rock garden plants by their nature grow in exposed areas. If you have trees and shrubs you need to be thinking more along the lines of woodland plants which will be happy in semi shade. A photo of the area you are hoping to turn into a rockery would help.