First of all, its purpose. No big secret here. It's right up front:
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.
Then, there's this little gem we federal attorneys tend to like:
This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding. Art. VI, Clause 2.
And, with regard to the public lands, which would include national forest and wildlife reserves. (I know because I missed this question on my law exam):
The Congress shall have Power to dispose of and make all needful Rules and Regulations respecting the Territory or other Property belonging to the United States. . . . Art. IV, Sec. 3, Clause 2.
Oh, and that militia thing? I won't even start with the "well regulated" one of the Second Amendment. Try this out in the enumerated powers Congress has:
To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;
To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress; Art. I, Sec 8, Clauses 15 and 16.
These and other provisions should always be considered in the light of nearly 230 years of Constitutional History which tends to reflect something I like to call "reality." Argue all the theory you want. I don't know any interpretation that justifies the armed take-over of federal facilities because you don't like the way the government of, by, and for all the People is operating.