Courtesy call
First off, the communication described is not what is known as a courtesy call; it is an initial contact. A courtesy call is entirely different. Unless chatter is slow I would recommend just your type and call sign/N # as applicable, followed by request or over. In busy airspace such as the LA basin or the northeast, never give the whole speil initially. You will likely tie up the frequency at an inopportune time or may even be in the wrong sector for the controller you are talking to. That aside, polish up the communication! It will pay off right away. Don't be a hot shot, just professional. You don't have to get paid to fly like a Pro... BTW, Phoenix does get busy at times but I would not consider that area busy airspace at all; they do have some great controllers though.