Here is a great book of Arizona trails. I have 4x4, not a huge off-road'r, but do my fair share when hunting. 4x4 is rarely required, more so when it is wet and muddy.
join every group/ club you can. Forums, facebook, whatever. it'll take a while to find a group of guys that are into the same style/difficulty as you. wheel with all of them.
I don't recommend going out alone, but if you must this book has solid trails and will keep ya out of trouble
https://www.amazon.com/Guide-Arizona-Backroads-4-Wheel-Drive-Trails/dp/1934838195
I don’t live in Arizona, but my dad bought this guys book for California in the 80s. He has new ones and I use them for California. He has an Arizona book. I would strongly encourage it.
https://www.amazon.com/Guide-Arizona-Backroads-4-Wheel-Drive-Trails/dp/1934838195
A day pass is required only if you stop in the picnic area. If you drive through and to the ORV trails no pass/ permit is required.
There are some trail maps available online.
If you plan to explore more of AZ offroad, this book is a great resource.
Congrats on the new Jeep! If you're moving out to Tucson, you may want to check out Guide to Arizona Backroads & 4-Wheel-Drive Trails 2nd Edition. It's a great intro to some places you can go.
New to the offroading world. What's helped me a ton is AZoffroad.net and the Guide to Arizona Backroads & 4-Wheel-Drive Trails Book by Charles A. Wells
Guide to Arizona Backroads & 4-Wheel-Drive Trails 2nd Edition https://www.amazon.com/dp/1934838195/ref=cm_sw_r_cp_api_glt_fabc_5NSYRHR738PCEYKD8TF2
Too many trails to list. Sunflower mine loop is one of my favorites. Martinez cabin, box canyon, Coke ovens. Or if you really want an adventure out of the way you can roll through the chirachouas not sure if I spelled that right. There's a couple really nice books with trails in Arizona that I use. I don't really use apps because the lack of cell coverage on the trail. But the books you can physically take with you.
https://www.amazon.com/dp/1934838195?ref=ppx_pop_mob_ap_share
https://www.amazon.com/dp/1946494143?ref=ppx_pop_mob_ap_share
I have used these books for years. Should be a must have for anyone in CA, UT, AZ, and CO.