I love Joshua Tree. I lived there for a bit, and have spent over 100 days in the park. I know it really, really well. Are you going to camp in the backcountry, down the Boy Scout trail, or in one of the campgrounds? The best campground is Hidden Valley, but be aware that it is very difficult to get a site on the weekend. If you're headed into the backcountry, try to find the Valley of the Kings...it is magnificent.
There are all kinds of amazing things to discover in J Tree. Oh, and if someone drunkenly comes through Hidden Valley at around 1:00 am shouting CHASM OF DOOM, drop whatever you are doing, get up if you were asleep, and follow him and his followers for one of the coolest experiences of your life, no flashlights allowed.
As far as what you need? That all depends on if you're backpacking or car camping.