Getting a car

Being a US Citizen and having a valid US Driving license (presumably), you need to get your residence visa first, then you can transfer your license to an Emirati license, all you will need is 650 AED approx + vision test.

Getting a car is easy, if you buy new, the showroom will take care of red tape for you, same if you buy pre-owned from a dealership.

If you buy used from a current owner, you need to visit any registration site, have the car inspected, pay the fee, insure the car ......and that's it

Gets a little more complex if you buy a car that is currently financed and/or if you want to finance the car

There is no red tape in getting a car.  If you are an USA Driving License holder, you can drive straightaway with rent-a-car.  Try to bring an international D/L along with your local D/L.  Once your UAE residency formalities are done, you can obtain a formal UAE drivers License.  Yes there are expenses related to purchase of a car!