A cooler.
Other than the normal stuff to get you unstuck, there's no real predicting what you may break. At one event, we had a guy sink his truck in a pond, which hydrolocked it. Man we had to raid about five different trucks in our group just to come up with enough tools and oil to undrown that engine. Its hard to predict, you will need a spare tie rod.
The best spare you need is a buddy who can tow you or take you out to where you can get something to tow you. All the group outings we do, we designate one or two vehicles recovery vehicles, usually a diesel with wench and tow straps.
The trick to offroading is don't break your vehicle. Pay real attention even if you have to buy the park map to not take it on trails not rated for your jeep. Limit your off side fun stuff to what you either see others do or slowly progress from easy to harder.
When I bought my first 4x4, I bought a Jeep Wrangler. I was so impressed I took it out day 1 in the snow. At one point, I ended up on the tip of a point, a sheer drop on three sides, and no room to turn around. It was then I remembered, I hadn't made a single payment on that Jeep yet. That's a God awful feeling.
Anyway we have a saying, we take these things out there to see how we can get them stuck or break them. Plan accordingly. To just explore the woods, all you need is a cooler and some commonsense.
Other than a tow strap, shovel, and axe, if I had to name the one thing newbes should take it would be radiator stop leak. You go down that trail too fast and hit that big ole fallen tree or rock, that babies going to bottom out and enough shock that radiator will pop. Stop leak will get you home.
Tj