Some great suggestions already.
I spent a lot of time in the Southwest, both in the "way back machine" and in the past 10 years. A few things and then just a route to get you in the area that I enjoy.
Depending on the time of year you will be traveling, you will need to plan ahead. There are a lot people in the area at certain times of the year - and I suspect a lot more this summer - and it pays to plan at least two/three days ahead, even for campgrounds.
It is easy to cancel most hotels more than 24 hours out, often very difficult to find one.
Carry a lot of water. Any issues that occasions a roadside or more remote emergency can get ugly early without water. Rule of thumb if you are not moving about is a gallon a day per person.
Also carry a tarp to make shade. I used to fly into Las Vegas and then take back roads to NAS China Lake and always carried the above.
One more thing. I know a lot of people that travel a lot in remote areas of the Southwest. They always rent a sat phone. Very cheap insurance:
https://www.roadpost.com/iridium-rental-plan-comparison
I'll post a recommended route in another post.