I've been 5 times and have stayed at a different place each time. Portal RV Campground was pretty nice. We stayed at a remote camp ground, but I don't remember the name. It was remote though! It was in the Hells Revenge/Porcupine Rim/Fins-N-Things park.
Other times we have stayed at hotels and one other camp ground in the middle of town, but I apologize, I can't remember its name. The showers are nice, so look for a place with those!
We are heading out again hopefully in the Spring and are thinking about staying in a Cabin this time.
Trail wise, it's difficult to run multiple trails per day because of how far apart they are. It's doable, but realistically you get about one trail in a day. The exception is the Poison Spider Loop- which is incredible! You run Poison Spider Mesa, Gold Bar Rim, and Golden Spike in one day. It took us about 12 hours with a group of 6. We tried every obstacle, fin, and ledge we could find, which added to the time and also stopped for a lunch. The quickest I have seen people get through i is about 9 hours wit no break downs.
My trail suggestions would be:
Fins-N-Things as your very first trail. It is the best intro into slick rock crawling.
Poison Spider Mesa
Golden Spike
Hells Revenge
Cliffhanger
Pritchett Canyon
Moab Rim
Behind the Rocks
Pritchet and Behind the Rocks are pretty intense. I don't know the driver skill level of your group or how well built your rigs are, but you need decent rigs and above average driving to get through those.
Everything in Moab is the exact opposite of wheeling i the South. Because the surface is so sticky (when it's dry), you can take 200hp and 32"s up hill climbs that you would need 500hp and 42"s to climb down here.
It's all about low RPM crawling. Straight up, straight down, over ledges, way off camber, exact tire placement.
Last piece of advice- take a million pictures. You will see some of the most spectacular views imaginable out there.
My wife standing in The Hot Tub on Hells Revene:
Just a random shot from the top of Gold Bar Rim:
Entering "Escalator" on Hells Revenge. My favorite obstacle in Moab.
The entrance to Pritchett: