Obviously if you will be camping for a week, some form of shelter will be needed. At its simplest this means a tent. At the other end of the spectrum is an RV. Burners are highly creative people and you see many styles of shelter at the burn. A shelter provides a place to sleep, store your crap, and escape from the elements. This is just a rudimentary discussion to get the gears turning - search eplaya and google for more detailed information on these.
Dust and wind are the common issues, and on rare occasions some rain as well. First and foremost, your structure will need to be able to withstand wind gusts over 60 mph. Optimally it will have a way to seal out dust as well.
The most common shelter used in BRC. First, discard the crappy little tent pegs supplied with yours. Any pegs used on the playa should be at least 12 inches long. Rebar or military tent pegs are common favorites. You will want to either buy a tent with no mesh vents or cover the mesh. Popular mesh coverings include sewing blankets over the mesh areas or spraying over the mesh with rubber bed liner (used on pickup truck beds). Optimally your tent can be covered by your shade structure to keep it from heating up in the early morning. For additional strength and wind resistance, add a few guy lines when setting up.
Place some heavy things inside your tent if at all possible. If your tent breaks loose in the wind, it could be dozens of miles away before you even know it's gone and you will likely never see it again. More importantly, if it goes airborne someone could get hurt.
The typical small box truck rented for moving can be a good shelter if set up properly. In 2012 we went the box truck route and it worked out well, aside from slipping off the back of the truck and fracturing my wrist after the temple burn. Eplaya has some very informative threads about this.
These are hard sided structures created from sheets of rigid insulation using simple straight cuts and a special tape. A bit more complex than most first timers choose to attempt, these are also bulky to store and transport.
Commonly called Bucky Balls, domes can be awesome shelters. They are a lot of work to make and assemble though. The most common structural material for these is electrical conduit, but some build them from pvc pipe. There are several common variations, and I suggest that if you attempt this route doing a lot of research.
RVs or Recreational Vehicles is a term loosely applied to mobile, self contained living quarters such as campers and motorhomes. They can be rented, but are expensive and consume massive amounts of gas (8 mpg if you are lucky).
Advantages - comfort, shower, toilet, kitchen, dining area, refrigerator, air conditioning by day, warmth at night, and a comfy place to sit out dust storms.
Disadvantages - expensive to rent, high fuel consumption, not fun to drive (especially in areas of high cross winds), more mechanical things to malfunction, and heavy fees paid if not returned in clean condition.
My experience - we rented one for our first burn. We booked it in January after getting tickets and the closest we could find was in Salt Lake City, Utah. Between the rental and gas it ran us about 4,000.00 for the week. We didn't use the air conditioning or the heat, the refrigerator was almost useless, but we did sleep and cook in it and use the facilities. Was it worth 4k? In my opinion no, and we will be tenting it from now on.