I like the way most of you think.
I have 2 sets of kids- 2 in college, and 3 younger ones. I get to make the mistakes with the older ones, then try again with the younger ones.
I made the mistake with the older ones of "letting them drive" one of my cars. Cheap beaters. But even so, it led to entitlement thinking- they came to think a car was somehow their birthright. As they got older, the transition out of it became harder and harder. (Who's insurance, which repairs, etc. etc.). I eventually gave each of them decent transportation beaters, mostly for selfish reasons- I couldn't get out of the patterns we had developed.
The problem was of course exaggerated by the fact that most of their friends DID get pretty nice cars from their folks, most expenses WERE paid.
The other thing that made it a bit more difficult was that we live in a rural area- no mass transit, bikes not an option. Additionally, the insurance burden was ALWAYS going to hit my account, whether or not they had their own (in GA, as long as they use my address as their permanent address, my rates increase). That won't change until they get their own houses.
One of them was a lot more appreciative than the other.
Next time around I WILL NOT provide anything. I like the idea of matching their funds. Partly because I retain a bit of influence (to get a safe car, etc).
One of my favorite cars for my kids was our '98 Impreza wagon. Good safety aspects, decent on fuel and expenses, handled well enough to learn well, 5 speed. Looks like crap (been hit multiple times, has mismatched panels, etc.), but looks brand new under the hood. Both my kids learned to drive on it. Not much in the pride or showing off department, but a great basic transport appliance. I'll be looking for something similar for my younger kids.