Welcome to the desert and glad you came. Tree selection is going to be critical for you, so be picky about what you plant. Despite this list, the best method is to take nature hikes and gather seeds from the trees that are already there. Then spread those seeds in swales over winter. That is the easiet, most cost effective, and has the most long term success. This is my short and non-exhaustive list of what grows in less than 10 inches of rain in zone 7b
-Pinyon pine: nut tree, but may require some shading on the south side to get going.
-Rocky mountain/utah/alligator juniper: get some berries from this which turkeys love. At the very least it can act as a windbreak and start building soil.0
-New Mexico Olive: AKA stretchberry or NM privet. This is the American version of the olive.
-New Mexico
locust: this is your prime nitrogen fixer.
-desert mahogany: also a nitrogen fixing bush
-false indigo: nitrogen fixing small tree with beautiful purple flowers
-three leaf sumac (rhus trilobata): edible berries
-goji berry
-maybe mesquite if you are in a hotter area (also a nitrogen fixer)
-also if you are zone 7 and have a runoff wash zone, then you could try almond, pistachio, or pecan planted into depressions.
Other shrubs:
-apache plume: nitrogen fixer
-sage: nitrogen fixer
-rabbitbrush: pollinator
-prickly pear: if you get some cash then you can order a spineless version, otherwise get seeds and whole plants from hiking around.