To buy or operate a standard car, one will have to be 18 years old. Under that age, adult supervision will be mandatory. This means the adult must be in the vehicle with the underage driver.
To buy a sports car, you will have to be 21. A "Sports car" will be defined as any combination of any two of the following: 2 doors instead of 4, spoked rims not requiring hubcaps, aerodynamic effects such as spoilers or air dams, a wheelbase under 100 inches, a manual transmission, a curb weight under 3000 lbs, fiberglass or other non-metal construction, or painted logos.
For every purchase, you will have to fill out a questionnaire confirming you're a US citizen, do not use drugs or abuse alcohol, have never had a conviction for alcohol related incidents or reckless driving. Lying on this form will be punishable by 10 years in prison and/or a $10,000 fine.
New cars will only be purchased from Federal Automobile Licensees who must provide fingerprints, proof of character, secure storage for all vehicles, and who must call the Federal Bureau of Motor Vehicles to verify your information before purchase. They may approve or decline or delay the sale. If they decline, you may appeal the decision in writing to a review board. If they delay, it becomes an approval automatically after 10 days. However, the dealer may decline to complete such a sale in case of later problems.
Read the whole thing. He makes a good point, which is that lots of people probably don't appreciate just how heavily regulated guns already are.