Does the constitution tell us what goals the government should serve

Yes, the United States Constitution states that a "We The People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America."

It also states that "The United States shall guarantee to every State in this Union a Republican Form of Government" 

However, this shouldn't be confused with the purpose of government, which is written in John Locke's Second Treatise of Government but is also stated in the Declaration of Independence. "That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed,"

To make clear the difference and avoid confusion Constitution states WHAT the government's goals are and the Declaration of Independence states WHY the government is there in the first place.