Congrats on the new jeep and welcome to the family!!
Fire extinguisher never hurts to have handy.
This is the list of trail gear that a club I wheel with would prefer you have if you are going wheeling but as far as tools, I carry my tool box with me whenever I go out and always have a big box of fuses just in case. That said, you kids with your fancy new jeeps may not need quite the same amount of crap as my YJ.
First aid kit
Extra Prescription Meds in case you get stuck out there
Fire extinguisher (A,B,C, type is reccomended)
Basic Tool Kit for simple repairs like removing your tie rod
ie socket set and a screwdriver set and an adjustable wrench
Durable work gloves
Air compressor to (air up!)
Tire deflators or a key ( air down)
Air guage (to see where you aired down to)
A gallon per person per day of water. Just in Case
Tow strap and tow points
Good Spare Tire
Jack (If you have a lift/bigger tires, your stock jack may not work)
A change of clothes (consider unexpected weather changes)
MRE or extra food in case you have to camp unexpectedly