I live in Carson City, NV, and have made many trips to or through Phoenix. The total trip is about 734 miles.
From Reno I would suggest:
I-80 east to Fernley
Alt 50 to Fallon
Hwy 95 to Las Vegas
Hwy 93 to Phoenix
As far as stops, I would recommend an overnight in Beatty, NV, at 331 miles.
Beatty RV Park Nothing fancy, but 50 amp FHU for $25.00 per night.
I would then fuel at Area 51 Alien Travel Center, 2711 E. Hwy 95, Amargosa Valley, NV.
The drive from Beatty to Phoenix is about 403 miles.
The above route and stops will allow you to drive through LV mid morning to early after noon when traffic is lighter than rush hour without needing to stop.
If you choose to overnight at Las Vegas that's about 449 miles from Reno, and you're bound to hit the LV evening rush hour traffic. Then when you leave in the morning you'll hit the morning traffic rush.