I was the same age when I bought my first car in 1963.
It was a 1933 Austin 10 which would have been a convertible if had had a hood to put over the frame. Cost £10 for the car and another £10 to have it transported across the Black Country. Pre MOT days when it was not unusual to see a Morris Minor or A35 with a dropped front corner where a king pin had broken. And the A series engine had already been around 10 years then.