Personally I think having AAA in AZ is super important. Kinda like the IL snow.. Well we have the heat! And that can be deadly! You do not want to be stranded in it. So as a former AAA agent can I give you some simple tips?? Always have a working cell phone, your AAA card, and ALWAYS have a cooler with drinks in it! That is just as important as keeping a blanket in your car in IL in winter.
Oh and WELCOME to AZ! Where are you moving here? Personally I love it out here! In spite of the 115 degree July days.
Oh and one more AZ tip... Really keep an eye on your tires.. They do not like AZ pavement and tend to blow.. And your car battery will only last about 2 years here- so be prepared!