Since you're interested in Zion, the Grand Canyon, and Antelope Canyon, I'll make a suggestion. In our new guidebook, RoadTrip America: Arizona and New Mexico: 25 Scenic Side Trips, I describe a route, Scenic Side Trip #13, that might be perfect for the beginning of your trip. It starts at an exit off I-15 in St. George, Utah (a couple of hours northeast of Las Vegas), goes through Zion National Park, then takes in the NORTH rim of the Grand Canyon, before passing through Page, and ending in Flagstaff at Interstate 40. From there, you'd have an easy drive west into California. Many people who are "in the know," (including myself) prefer the North Rim of the Grand Canyon, because it only gets 10% of the crowds you'll see at the South Rim. Here's a link to an RTA Interactive Map that wil show you what Scenic Side Trip 13 looks like. You can find more information about the book here, and you should check this post in my blog, Antelope Canyon: Part 1 for the inside story on that truly fabulous geological marvel.
Good luck with your planning! You're going to have an amazing RoadTrip, regardless of which route you choose.