We flew into Vegas and did the opposite loop. I don’t think it matters which way you go, it just worked out which way we could get campsites. We did 2 nights Grand Canyon, 2 nights arches/Moab , 3 nights Bryce (one of those nights was a hotel, cleanup, pool time for kids) and 1 night Zion, 1 night Vegas. Our kids are young so depending on your travel group may change opinions.
Our favorites were 1.Zion 2.Arches 3.Bryce 4. Grand Canyon. We LOVED Zion but it was extremely crowded and some of the best hikes the kids needed to be a bit bigger for. Arches was beautiful and had great hikes for the kids. I agree with another poster that in March your weather will probably be the best at Zion and Arches as it will be a bit warmer. Bryce was lovely and the queens Garden to Navajo Loop into the Canyon was really neat but i could see where it would be chilly in March. It got down into the 40s at night last week. Obviously was warmer during the day.
I would say we were least impressed with the Grand Canyon. It was neat don’t get me wrong, but there weren’t any hikes the kids could do so short of looking at it, and touring the visitor center, it could be done in a couple hours. I don’t know if it’s worth the nearly 4 hour drive. I’m glad I saw it but I wouldn’t have to go back anytime soon. We did the south rim. I’m happy to answer any other questions!