This is the first direct allusion by Milton the hierarchy of Hell possibly being connected to Milton's own thoughts on the monarchy. Milton is primarily using the Matthew 12.24 description of Beelzebub as "the prince of all devils." Milton keeps with the consistency of the legend of Beelzebub with this.
Milton also attempts to show us the residues of the fall. The fallen have ended up in what was much of the same hierarchy that was set in Heaven when they were angels. Milton is making another attempt to show that while the angels are fallen they still think of themselves and appear as beings who have not sinned and are still under God's graces. Milton attempts to show the reader that while all the angels have fallen, when they are received into Hell, they are not all of the same level. It would seem that here in Hell those who are perceived as the "most right" in Hell are those that are most evil or most against God in reality.
Along with this is Milton attempts to show some of his convictions against the monarchy. He attempts to show Beelzebub not in a tainted light, and by using prince in a way that to those in Hell is positive but to those reading is negative because of where they are. The angels have escape heaven due to the tyranny that God created as a ruler, yet the first thing they do is set up this monarchal system in the realm of Hell.
Counsel here means Beelzebub is the wise advisor to all the fallen in Hell. Milton sets up a sort of false prophet in Beelzebub, giving forth the words of and plans of Satan as the truth. While he is appearance is princely, he is also counsel to not only Hell itself, but as counsel to Satan as well. Satan being parallel to the "king" of Hell, he is a sort of royal or King counsel to Satan, and where Satan may not demand as much respect, the way Beelzebub is described, he commands respect unlike any other.
The word "shone" alludes to his former glory as an angel, directly relating to light and heaven. However this shines not on him or his soul but through his face, thus explaining a certain vanity that is associated with the fallen in Heaven, the thought that they are still a part of Heaven, even as they have been banished to Hell.
-Erik Scott