Final answer:
The luxury train that started service between Sydney and Melbourne in 1937 is The Spirit of Progress.
Step-by-step explanation:
The royal blue luxury train that started running between Sydney and Melbourne in 1937 is d) The Spirit of Progress. This train was known for its luxurious services and speedy journey, offering travelers a premier way to travel between two of Australia's largest cities. The Spirit of Progress represented a significant development in the Australian railway services, becoming a symbol of modernity and efficiency in train transportation at the time.