I-15 to I-40 is more direct than going through Phoenix, plus you'll be approximating the old Route 66, for what it's worth. A potential side trip is to stop by Laughlin, Nevada, a low cost casino town on the Colorado River. It's about a 20-30 minute drive off of I-40, and rooms in quality casinos like Harrahs can be had for less than $40 during the week.
Another option is to try the Amtrak Southwest Chief, which has overnight trains running from Fullerton (FUL) to the Flagstaff (FLG) and Grand Canyon (GCN) stations (and beyond to Chicago). Of course this requires that you be able to sleep on a train, which is iffy for most people I believe.