I was only in Moab one day this summer on a roadtrip and I did Fins n Things in a stock 3rd gen 4runner (A/T Tires). Super fun trail, but definitely more pucker moments than I would have cared for. That was mostly from lack of trust the slickrock for the first time. No trail damage at all at stock height with sagged rear springs.
There aren't any bad ones. Stick to the 1-4 trails on Trail Damage or easy/intermediate trails in Well's book if you are stock and/or unfamiliar with the area.
There are so many it's impossible to say, all depends on what you want to do. We did trails rated 2 and 3 that were intended more for the scenery but still offered some challenging spots and they were amazing. Chicken Corners, Secret Spire and Copper Ridge. Here's some pics:
I would recommend getting on the red rock 4 wheelers website and checking out trail descriptions and ratings. Rr4w.com or something like that.