I drove one of my parent's cars in high school and didn't have a car my first semester of college.
My first car was a 1988 Chevy Cavilier 5 speed and I split the cost 50/50 with my dad and paid my own insurance. It was titled and insured in both my name and my mom's name so the insurance was cheaper. I drove that through college until it died after my first year of law school. Dad then helped me again buy another car 50/50, a 1992 Geo Prizm and I paid insurance again.
Both cars were under $3000 so I paid $1200 to $1500 for my half. I couldn't have bought a reliable car without dad's help. They were always 8+ years old but dependable. And tiny, I could parallel park in just about anything, LOL.
My husband couldn't fit in the Prizm (he's 6'6" and the prizm is tiny!) and after we were married, my dad sold us my grandpa's 1991 Mercury Grand Marquis. Not a hip, sporty car for a young married couple, LOL, but very dependable. DH drove it to his first teaching job which was 25 miles out of town. His old car would not have been good for commuting so I drove it to school and my part-time job in town. Again, we went 50/50 and we paid $2500 for our half. I was still in law school so I think that's why my dad helped us out.
Since then, we've bought our own cars. But it was a wonderful thing to have help. Since my parents paid for part, I felt it was part their car and took really good care of it. I also felt ownership in the car because I paid for half out my savings account and/or with my 2 or 3 summer jobs.
I know we will help our kids with their first car, too. Nothing new and nothing fancy. Reasonable and reliable.