The best cars to do this journey are obviously the 4WD.  But is not necessary to be a super equipped 4WD as we used to see in the rally Paris-Dakar. However it does help that they be provided with carter protections, a snorkel also can protect the engine from the dust. However nothing of this is really necessary for carry out the journey. 

We advise vividly to do a checkup to the vehicle before leaving.  If you have a vehicle that constantly gives you problems and it needs mechanical intervention perhaps it's not the bestl vehicle for this journey.  In the desert there aren't repair shops and too many stops will delay the group. 
It is relatively easy find parts for Peugeot, Mercedes, Land Rover and Toyotas. We're talking about the basics, no fancy electronics or sophistications.