"appropriate" is a loaded and subjective word. Further, some government activities and programs could be widely viewed as appropriate up to a point.
That said, we generally expect our federal government to:
establish a monetary system
maintain economic stability with respect to employment and inflation rates
enforce public and private contracts
protect markets from corruption and malfeasance.
allow markets to operate openly and efficiently
provide safety nets for the misfortunate.
etc.
What is the appropriate role for government in the economic system?
That depends upon which economic system you embrace. Please post your answer and we'll be glad to critique it.