Please BUY LOCAL WOOD!!! Bringing wood from another area can lead to invasive species being introduced to an environment(plant and animal).
Moab is an incredible place that Im lucky enough to call my backyard. The key to packing for a multi-day trip with limited space is knowing whats available along your route. The more remote your trip, the more you will be required to carry with you. With a destination like Moab, you just need the minimum since most things will be readily available once you are here. A hitch receiver basket adds a LOT of space to a TJ too.
Shelter: Tent, sleeping bags. March still gets pretty chilly at night and I have been snowed on a few times in Moab in late March. Sleeping pads might be required depending on where you camp.
Water: A 7gal jug will be a good thing to have at camp. You can refill all water bottles for free at Gearheads downtown. You will want smaller bottles for trail use.
Food: City Market downtown... you will most likely pass right by it going from camp to the trails anyway, just swing in and get what you need daily. No need for a giant cooler. Theres also about 40 restaurants in town for whatever hot meal you dont want to cook yourself. My favorites: Zax Pizza, Moab Diner, Milts(Burgers), Blue Pig BBQ, Moab Brewery and Gilberto's Tacos.
Camping: You will need a portable toilet to camp off grid but there are plenty of campgrounds with vaults for ~$15/day. The spots along the Colorado River get windy and always have road noise. Go West at McDonalds and drive out Kane Creek to The Ledges Camping area. Way less people and still only 10min from town on one of the most beautiful dirt roads known to man.
Trails: I tell everyone to start out with Fins N Things for the true Moab experience. Traction is unbelievable on the sandstone and the trail is a ton of fun. Hurrah Pass and Chicken Corners is another "must do"... and its even better if you stay at The Ledges campground sing you are right at the base of Hurrah Pass. The FunTreks book by Charles Wells is probably the best guide book for the area for more trails.