re: The Mighty Five - Utah

Yup. Went in May of 2015 from Athens... drove in from New Mexico and Colorado into the southeastern corner of Utah up to Moab. It's doable in a week certainly, but you won't see everything each park has to offer.

My favorite of the 5 is Capitol Reef. It's the most remote of the 5, the least visited, and IMO the most surprising beauty wise.

As for suggestions... just do it. See them all. Hit the highlights of each.
To see them all in a week:
Arches - delicate arch hike & devils garden
Canyonlands - islands in the sky scenic drive, maybe gooseberry canyon
Capitol Reef - scenic drive, burr trail road or notom-bullfrog road, orchards, cathedral valley, capitol gorge hike (tanks), hike to the halls Creek overlook on the south tip of water pocket fold
Bryce - hike down into the amphitheater, around the hoodoos, Bryce point, and rainbow point
Zion - the narrows and angels landing

Weather in April is sketchy... it's that time of year that a late winter storm could hit, or it could be warm and sunny. It's best to play it by ear and keep an eye on the weather a couple weeks before you head out.