In my opinion, you should get your own car (that you pay for yourself with your own money) when you are in the early or mid twenties. However, as a young adult (18-20 yrs old), you might want to think about asking your parents to use their car from time to time. :)
One thing to keep in mind is that: Very expensive insurance, “assigned risk”, is normal for any driver with no “Insurance history”. It’s three times as expensive as normal. 3 years of insurance history, (no big accident) helps a lot. You get out of the “Assigned Risk” category. Then over 25 years old, rates drop down to normal. Being on your parents insurance as an occasional driver for 3 years creates insurance history. (That would be true even if you seldom drove your parents car). For a car in your own name: Having a cheap, replaceable car for the first 3 years, would make it unnecessary to pay for collision insurance, on top of the state mandatory liability insurance. Like a $3000 car plus get new tires and brakes battery tune up... With no collision insurance, if you crash, you must fix it or replace it yourself, unless you get hit in the rear, for example, then the other driver’s insurance must fix your car. 3 years of no collision insurance can save $3000. Check the rates.