1960 was 50 years ago, how time passes... anyway that it kind of tall order. If you are 16 or 17 age and looking for a new car just to get to and from school I would recommend a late 90s honda/toyota, this was the golden age in reliability/quality for those cars. The trouble with the 35+yr older cars is that they used some very old engine and fuel management technology. You would really need an old mechanic that was around back in those days to recognize the nuances and intricacies with those cars. They do no carry an OBD0/1/2/3+#* system to give mechanics fault codes to at least have some first clue as to what the problem is, you had to play it all by ear/smell/experience.

Life is short, I have myself have had the unfortunate circumstance of being stuck on the side of the highway and street due to an engine or ECU failure. It is not a fair situation to put on a  younger person, those situations can quickly turn deadly without the right experience.

Beautiful cars, but ancient by car standards. Don't expect to be able to daily drive that or put several thousand miles a year on it. 

Anything that old is gonna need a lot of love and money to keep it running unless it's been completely overhauled. 

I wouldn't recommend it unless it's just a toy/weekend car. 

Do you know what the accident rate is for kid's first cars? Check it out - https://www.cdc.gov/transportationsafety/teen_drivers/teendrivers_factsheet.html

A. A Cadillac from the 60's is not safe for the occupants, has terrible brakes by modern standards and will be expensive to repair - IF you can get parts

B. Whatever you get for the kid, get them AAA coverage and make them pay for the insurance

69 Camaro SS with the 396 CU engine.