About 6 years ago, my husband and I did a similar trip to yours. You can find it here. We started in San Diego, but we came right through Phoenix and Flagstaff.
We found that fuel was not at issue. We have a tendency to fuel up when we were in a larger town - Flagstaff, etc.
Cell service was mostly okay, though it was very spotty when we headed to the North Rim of the Grand Canyon (and pretty much non-existent, there), and in other national parks. There were many times when I was at "3G" service, though, so I saved anything I really needed, for the overnight lodging.
I don't keep up with the Utah parks, but I think Zion may have timed entrance or the requirement to use their shuttle. You might check their website to be sure.
Donna