The foam board you are seeing at Lowes in 1" 2" and other sizes is pure junk for your application. It is used for insulation. It will tear up before you get it on the door. Get rid of that thought.
The ABS sheet stock you can buy at a lumber yard is sold under shower panels. Unless you have an almost flat surface, forget it. Very stiff and hard.
Luan is only fair to use, almost as bad as cardboard products when wet. If you don't think you are going to get it wet, look at where the water goes when your car is rained on. Right down the bottom of the window and then right on the back of the panel. Don't kid yourself, it will get wet. Wonder why new cars come with plastic film over the door when you take the panel off, most think it is for dust control. Wrong, they don't want water to even bother with the plastic panels and glue they use. When you do your door, take a hint from them and tape a plastic film across the opening on your doors under the panel. 2 minutes and lots of protection..
Now, the best material for your panels: PVC foamboard. It is not polystyrene, nor is it plexiglas, it's foamed poly vinyl chloride which comes in 4' by 8' sheets. It has a film encasing the closed cell foam and you can use heat from a heat gun to bend it or form it to the curve of the door. Water does not effect it. You cut it with a knife or scissors. You won't find it at Home Depot or Lowes, you need to go to a plastics supplier, sign shop, or upholstery shop and ask for it by brand names of Sintra, Komatex, CelTec, or Palight.