Because this idea is a "Christian-ese" concept that has traditionally been used to explain the heart of the Gospel with respect to the law, any answer here that Biblically explain this view will not necessarily "support this viewpoint." Much like T.U.L.I.P and the seven dispensational epochs, concepts like this tend to oversimplify Biblical truths. This doesn't mean it is unbiblical, but that it should never replace the Biblical foundation it stands on.
Moral Law:
Jesus gave his own interpretation of the law in His Sermon on the Mount, but without the epistles, early Christians only had the Old Testament to deduce what part of God's commands were part of our training toward maturity (our tutor in Gal. 3:24), and what parts reflect the Law of Liberty in Christ (Rom 8:2). Jesus' revelationary [sic] contribution to our understanding of Moses' law tells us that we are not to disregard it completely, but we need to discern which parts of the law were established for our "upbringing," and which they would have to preserve in their new life with Christ. When Jesus said "You know the commandments" to the rich young ruler in Mar 10:19, he was likely talking about the Ten commandments, or more broadly, the "Moral Law" of Moses. Even with our death to the law (see Rom. 7:4), our obligation to be like Christ does not change.
The Prophet David says in Psa 40:6 "Burnt offering and sin offering You did not require," but this sounds contradictory since God literally did require it in Moses' law. But not forever. This example is a good distinction between where Moses' law and the Law of Liberty separate. God calls David a man after His own heart probably in part because he saw the difference. Other verses like this exist. See Micah 6:8:
He has shown you, O man, what is good; And what does the LORD require
of you But to do justly, To love mercy, And to walk humbly with your
God?
So, the "Moral Law" in our simplified tri-part system we're examining here are any of those commands about which David could not have said "you did not require." Most of these "required" laws, based on our David definition have a broader "Law-of-Liberty" version: Hate is murder (Matt. 5:22), idolatry is covetousness (Col. 3:5), but, as always, God's heart doesn't change.
Ceremonial Law
The letter to the Hebrews (especially chapter nine) reveals that much of Moses' law contained copies or patterns of heavenly truths. Just as there is an altar in Moses' law, there is a version of that in heaven, from the Priesthood, down to the altar and candles. These patterns given to us in Moses are "Shadows of the good things to come" (Heb 10:1), so they are similar to the Moral Laws in that they reveal a bigger truth. In this case however, the truths they reveal are not mandates of holiness. They are symbols of heavenly places.
So the "Ceremonial Law" in our simplified tri-part system, are any commands about which David could have said "you did not require," and were shadows of things to come, and were not primarily commands for civic functions. Not all these are in Hebrews, but it gives us a good starting point.
Civil Law
By process of elimination, I would say that these commands are those which do not adequately fit in the categories above, but, like your question states, called the Hebrew people to form a working society. In my opinion, it's really hard to separate this category from the Ceremonial Law without adequately defining "Civil" and "Ceremonial." Especially in a society where law and faith are never separated. Laws that talk about inheritance, land boundaries, and punishment for crime, might nicely fit here, but couldn't someone also say they point to shadows of things to come, i.e., the judgement and reward of God's people and enemies? Maybe, but again, this three-fold division is never explicitly made in the scriptures.
