No affiliation, but went off a lot of the green trails in this book with a grand cherokee and it was helpful to understand what we were getting ourselves into, as well as find new trails.
https://www.amazon.com/Guide-Moab-Backroads-4-Wheel-Drive-Trails/dp/193483825X/
If you intend on renting a jeep and want to drive some trails that won't put your life in danger, I would recommend the following:
Take Gemini Bridges road from Highway 191 (about 10 miles outside of town) all the way to highway 313 outside of Dead Horse Point state park.
This trail is well maintained, has plenty of signs, and you can stop along the way to check out the Gemini Bridges Arch (look up photos, it's pretty cool)
Once you reach highway 313 head South, check out Dead Horse if you would like, and then connect with the Long Canyon trail.
Long Canyon is a beautiful trail and it is well maintained. It takes you along the edge of the canyon where it eventually drops down to the bottom and takes you under a large boulder that has fallen and created a small tunnel.
This loop is convenient and awesome because Long Canyon will take you right back to Moab when it meets up with Potash Road.
All of this can be done in half of a day, and you will be back with plenty of time to eat at Pasta Jay's!
Additional awesome resources:
A must have jeep trail guide for Moab, I call it "The Bible"
A blog entry with Gemini / Long Canyon photos
Enjoy Moab!
EDIT: I've rented Jeeps in Moab and Outlaw 4x4 had the best rates. The rigs they give you are very capable (lifted lockers front and rear, etc)
As far as places to stay, the Bowen has good rates, The Slickrock RV park rents tiny cabins that are good, and the Lazy Lizard Hostel also rents small cabins if you are on a budget.
I can't get it to work because their website is cancer, but you can find it here.
You have take it with a grain of salt. I've seen sheds rolling down the street and the weather said it was only 25mph winds.