So, to recap, if we go with this newest idea, these are the magic types I'm thinking:

Universal Magic (any magical effect not tied to the Elemental Planes, the Infernal Abyss, or the Cosmic Void)
Fire Magic (powered using Raw Mana from the Elemental Plane of Fire)
Water Magic (powered using Raw Mana from the Elemental Plane of Water)
Air Magic (powered using Raw Mana from the Elemental Plane of Air)
Earth Magic (powered using Raw Mana from the Elemental Plane of Earth)
Infernal Magic (powered using Raw Mana from the Infernal Abyss)
Cosmic Magic (powered using Raw Mana from the Cosmic Void)
Chaos Magic (extinct form of magic without a known source, thought to originate with the gods)

Of course, none of our characters will touch Chaos Magic (at least not until much later on), but I included it because it has historical context within the world. I'm thinking the ultimate goal of Tiamat is to return Chaos Magic to the Mortal Planes so that she can be free of all constraints, and perhaps our characters eventually hunt down the Vestiges of Bahamut, which can be super-powerful Arcane Conduits that allow them to temporarily use Chaos Magic themselves to thwart Tiamat and her forces. But that's a long ways off, we'll worry about that when we get there XD. 

So, does that sound good to everyone?