There are quite a few masters that advocate the walk for connection and lateral flexibility no matter what your skill level is. Walter Zettle comes to mind in his book Dressage in Harmony.
I am a proponate of the walk and I do what I am going to do at the walk first, including but not limited to side pass and walk pirouette. Once I have the connection and foward, then it is on to the canter. It works well for us.
