Because you want something low maintenance in this environment of ours, you will want to stick with the native desert plants like the Palo Verde or Mesquite, but those are very messy and can get quite large if you don't stay on top of pruning. Nor do they have leaves that look like leaves. This is because it's a survival adaptation to our brutal summers. Less leaf real-estate means less evaporation and they can survive the summers without a ton of additional watering. It's also the reason the Palo Verde trees shed leaves and branches in the summer. Water conservation = survival.
If you want something that looks like a traditional northern tree, you will have to prepare yourself that you will need to water the sucker a lot so it doesn't fry in the heat, especially during the first summer or two until it can establish its root system. Think long super-deep watering to establish the roots. You will have to accept that trying to make a non-native species grow in the desert requires work and go into it with that mindset. Also, be prepared that these trees will probably shed a lot of leaves in the hot summer regardless and they may die even if you baby them. There are some lovely citrus trees that do well in our climate and don't get very large, but they require a lot of water and the fruit can be messy.
We are currently experimenting with some Sour Orange and Ficus Columns as large shrubbery to shade some south facing walls and green up some harsh spots in our yard. We plan on keeping them trimmed to around 10-12 feet high but they can both get much larger. The ficus has had a rough summer and has required extensive deep watering in addition to the drip timers but is still alive (yay!) but the Sour Orange has been thriving in the heat. We had to throw shade cloth over the baby lime and tangerine trees we planted in the spring because the sun was roasting them to death.
All in all, there are no perfect trees and you will have to decide what is most important, the shady leafy look or low maintenance, because you won't get both in Phoenix. If that still isn't acceptable, you may want to look into giant plastic fake trees. They probably won't shed and you won't have to water them