As @Tullochgorum said, the Simpson is a very dangerous area, but it certainly looks beautiful! It's broken down into many sections, and since I don't know your level of off-road driving, I wouldn't presume to tell you which would be best.
Disclaimer: I'm not an off-road driver, and have never been on this kind of trip, so everything in this answer will be from online research. I only quoted sources which agreed with other sources, so I hope that means the information is credible.
To answer your question about vehicles, a 4WD is absolute essential to have almost any possibility of safely crossing the Simpson.
A high clearance 4WD with low range capability is a must and it must be in tip-top condition. This is not a place for all wheel drives and “soft-roaders”. Have your mechanic give the vehicle a thorough check and service and ensure they know you are about to do a Simpson crossing so they appreciate the importance of the job they are doing.
This is not a trip to be taken lightly and you will need to be very well prepared. A well maintained and reliable 4WD vehicle is essential.
Some of the important considerations:
- Heavy construction for durability to drive through extremely difficult conditions. Those include things like rough terrain, potholes, unexpected areas of soft sand, fallen debris, sand-fog, sudden hills on one side of the vehicle.
Height of the vehicle, weight enough to support any modifications, and good suspension
Heavy duty springs and shockers and a lift are just about essential. A 2 inch lift is perfect, compromising the handling only marginally whilst providing good clearance.
Your suspension will get a severe workout when heading off-road. Aftermarket suspension is a good idea as long as you use reliable and reputable brands and preferably have it fitted by a professional. Shocks and springs in good working order will have a huge effect on how the vehicle handles both on and off the road. Ensure your suspension is adequate for carrying the extra load of your gear. Air bag suspension is a great addition for carrying heavy loads but, even with suspension upgrades, be careful not to go over your vehicles load carrying limit!
Proper tires and room to store extras
Make sure you have the right tires for the job. There is no point heading across the Simpson Desert on highway tires. A good set of all terrain or mud terrain tires is essential. Ensure you are using reputable and reliable brands and that you have plenty of tread remaining.
For remote areas, take a minimum of 2 spare tires and a puncture repair kit. For some trips, you may like to take an extra tire carcass, tire levers, bead breaker, tire gaiter and spare inner tube.
A large fuel tank and/or ability to carry extra fuel is essential. There are large spans of the Simpson without fueling stations.
Depending on where your last fuel stop is and which route you intend to take, you will need enough fuel to travel from 600 - 800 kilometers (approximately 370 - 500 miles). It's not nice smooth driving but high range driving over power sucking sandy tracks, dune climbs and probably some low range work for good measure.
Obviously there will be many factors that will contribute to your fuel consumption. Keep in mind that a good margin for error is required. Bad weather can require much harder going than usual, sucking even more fuel out of the tank.
A long range fuel tank is a great asset here, but not essential. If this is not going to be the type of trip you do often, the expense of a long range tank is probably not justified. The other option is to use fuel safe jerry cans. These come in 10 and 20 litre sizes and, especially if carrying petrol, should be carried on roof racks.
- Extra room to carry spare parts and fluids
The spares you carry will depend on the age of vehicle, but the most common items carried are belts, hoses, fuses and a fuel filter.
If any of these are close to replacement, then have them replaced before leaving and keep the ones removed as spares.
Essential fluids such as engine oil, gear oil, brake fluid and coolant should also be carried in remote areas, and some epoxy ribbon or paste can be very handy to repair small leaks in fuel tanks and radiators.
- Customized area to mount sand/safety flags, which are important across the whole trip, and mandatory in certain parts. In case you're interested, detailed flag requirements and specifications can be found here.
- Large enough to sleep in if you get stuck or tired on the long journey.
- As with any vehicle on a dangerous trip, plenty of room is essential for
- first aid kits
- extra clothes
- extra food
- emergency items such as flares
- communication equipment
- navigation equipment
If you do decide to make the trip, I recommend checking out this excellent three part series called Crossing the Simpson for beginners.
If you can't or don't want to drive it yourself, there are 4WD tour groups. They vary in length and areas of the desert. You can find a list here.
Other source material:
How to Cross the World's Largest Sand Dune.
Simpson Desert Conservation Park and Regional Reserve.
Camping South Australia.