I teach high school and I can tell you that teenagers are horrible drivers. At least once a week a student will tell me how they or a friend got into an accident, ticket or lost their license in court.
If you go with a RWD, teach them to drive it in a parking lot when it is raining. No matter what you buy them, put good tires on it. So many of the students have bald tires because they spent their money on subwoofers. I plan to buy my children FWD, low power cars. Teenagers race everything, we were all there at one point in our lives.
To the original topic, $2k is a lot for a car that does not run as a first car. Sounds like money is tight. Get a $1k honda or toyota and put $500 into tires, brakes, oil and your set. Not pretty, but reliable.