No. You shouldn't make it $2000. It sounds as though your plan will get you to $2000, when it is all said and done. I like your idea, I was treated that way growing up as well. I think, let him learn to drive in a car that is low power, auto, front drive. Let him prove his skill in a car that he can't get himself into alot of trouble. Teach him about "HIS" car fix it up, see how he progresses into it.
As for the car;
80's VW's easy to play with, cheap, mostly reliable, alot of them to be found in ok shape.
Good luck.