You've gotten some good advice... The Sunset Western garden book and the general idea of looking for native desert plants, that are adapted to your area. The school of landscaping based on using desert-adapted plants is called Xeriscaping (where the xeri refers to dry). If you google that or look for books on it, you will find tons of info.
For a few specific suggestions:
chamiso is a common desert shrub, 3-6 feet semi-evergreen and very tough and hardy.
Scarlet bouvardia (aka Firecracker bush, Trompetilla) 2-4 ft. shrub with shiny, oval, dark-green leaves and bugle-shaped red flowers, 2 in. long, the rim flaring into four segments. The flowers are arranged in clusters at the ends of the numerous erect branches. A shrub with brilliant scarlet, tubular flowers in loose clusters at ends of numerous erect branches.
The spectacular red corolla attracts, and provides nectar for, hummingbirds. The Spanish name, Trompetilla, which means little trumpet, refers to the corollas shape. https://www.wildflower.org/plants/result.php?id_plant=BOTE2
www.wildflower.org is the site of the LadyBird Johnson Wildflower Center at U Tex. It has a native plants database. Put in your state, what you are looking for (eg. shrub, herb, tree, etc) and your conditions (sun, part sun, shade, wet or dry soil) and it will give you an extensive list of native plants meeting those requirements.
There are many varieties of cholla, a beautiful cactus. The teddy bear cholla (aka cane cactus) is one with gorgeous reddish-purple large showy flowers
My sister lives in New Mexico. When I visit her out there one of the plants I love the most is the ocotillo. It isn't exactly a shrub, but a clump of long stems, each with a brilliant red flower spike on top. Sometimes you see them a few feet tall and sometimes they get up to 20 feet tall, but very striking in the landscape.
Those are just a few of my favorites of the 49 plants that popped up when I put Arizona, shrub, part sun, and dry soil into the searchable database.