does any one know the main source of private transportation in 1937?

Answer 1

Depends on the country. Remember '37 was the height of the Depression, so many were out of work.
In the US, in metro areas public transportation; usually a streetcar was the primary means intra-city.
In the country, and in 1937 the majority of the population still lived on farms and small towns, it would be either horse-drawn ,or possibly car/truck.
Inter-city/long distance trips were invariably done by train.
There were airlines, but air travel was reserved for the very rich, and considered quite a novelty.
If anyone owned a car, they would only have only ONE. Unless, of course one was well-off.
Europe
Intracity: Foot, bicycle, possibly streetcar, bus.
Intercity: Train, bicycle, bus
Cars were (and somewhat remain) more expensive per capita than the US, and were reserved for the upper-class. At this time, that term was very socially specific, especially in Britain.
This mindset is what made Adolf Hitler's decree for a "Volkswagen" "People's Car' so revolutionary in Europe.
In general, if you show people walking, taking a streetcar, or bus around town; and taking a train for long trips, you'll be dead on.

Answer 2

Probably a car...