Ive read a few peoples stories where they just had their tent/car and they had very less of an enjoyable time due to that.
You'll find stories about people who were unhappy because they brought more than that. Different people have different preferences.
Based on your questions I'm guessing you're not too much of a camper? For first timers the number one thing is to make sure you have the necessities to survive a campingtrip in the desert.
Shelter is an interesting subject and what is best depends on each individual. If you rent a trailer you will probably be tempted to stay in when the weather is not nice. Dust storms, heat etc. That can be a handicap since you might otherwise seek shelter in shelters of experienced burners and make some new friends. Making a shelter is easy. It can be as simple as some poles and tarps or a complex geodesic dome
http://desertdomes.com First time without a lot of camping experience you should go simple with your camp, make sure you have the things you need and enjoy the shade structures and company of the more experienced camps. If I was not experienced at camping and it was my first time I'd probably advise myself to rent a small vehicle that has fold down seats that I could comfortably sleep in. No need to worry about setting up a tent, wind destroying things. If you like to sleep late, you'll bake in your car, so that won't work, but you'll also bake in most tents.
Have you read the burningman survival guide? That is important.