My daughter doesn't work. She volunteers, and as a result, gets a free 2-year ride at the local community college to get all the basics out of the way before she goes to University. She's not bringing in a paycheck, but she is saving mom/dad a LOT of money in college fees. That was part of the deal in obtaining a new(er) car. That aside, she will begin working at a "regular" job this summer and through school as the volunteer work that earned her the 2 year ride will come to an end soon. I understand what you're saying about having her pay for a portion of the vehicle. That's what I did when I was her age. But, I also didn't go to college...rather, I went straight to work (well, I did go to a tech school for awhile). She's delivered on her portion of the deal. Now, to be able to put gas in the vehicle and go from point a to point b...she will need to work to earn money for gas...because ol' mom and dad aren't going to pay for that too!
As long as there's some sort of deal in place that taught/teaches your daughter about the opportunity costs/benefits of certain choices, you're doing the right thing. The last thing you want is for her to get everything she wanted without even batting an eye. That was my point.
Get her a Honda Civic (used or new) It will cost more up front, but it has low insurance, low maintenance, great reliability (peace of mind) and pretty good mileage. Also it's a very safe car in case of a collision. You might even consider the hybrid version. Also it has great resale value.