Congratulations, you have a great adventure ahead!
My college room mate (from the late 60's) and his wife did something very similar last Spring. They flew to Vegas, rented a "C" from Cruise America and joined us at Lee's Ferry in Glen Canyon NRA outside Page (We drove out from NC). Cindy and I have always camped and we've spent time in the Four Corners area but our friends were rookies and had never been out west. Our plans were to see the Grand Canyon and the Mighty Five but a month was just not enough time - we missed Arches and Canyonlands. We just had too much fun at the places we did go.
Since you're new to this, I'd also suggest reservations. Zion, Watchman campground (electric hookups, no showers). Bryce, Kodachrome Basin State Park (electric at some sites, awesome showers). Capitol Reef, Fruita campground (no hookups, no showers). Canyonlands and Arches, you're veterans by now so try dry camping at the Horse Thief BLM campground off Hwy 313 between the two Parks (no water, pit toilets but clean) or Dead Horse Point State Park if you still need hugs.