I'll be adding a few more things to this list, especially in the non-human sections, but this is what I have planned out at the moment (minus a few things that I thought were too spoilery).

Basic

EarthFireLightWaterWind

Variant

CloudLightningShadeSoundStone

Combination

Combinations have a synergistic effect. Magic users with combination type affinities can use each of their component magic types (though not as well as a pure affinity can), as well as using magic unique to their combination.

Blizzard (Crystal + Water + Wind)Blood (Life + Water)Clay (Earth + Water)Firestorm (Fire + Wind)Flare (Fire + Light)Ice (Crystal + Water)Lava (Earth + Fire)Metal (Crystal + Earth)Mirage (Light + Water)Sandstorm (Earth + Wind)Snowcloud (Cloud + Crystal)Storm (Water + Wind)Swamp (Earth + Water + Life)Thunderstorm (Lightning + Water + Wind)Wood (Crystal + Earth + Life)

Rainstorm - Nickname for storm affinities with a strong water primary.Windstorm - Nickname for storm affinities with a strong wind primary.

Arcane

Chaos - This is currently considered an arcane type, but it might be subject to reclassification once it's better understood.CrystalLifeMentalNull - Technically, this means no affinity, but it's considered an arcane type for classification purposes.Void

Spectral Beast Magic Types

Replication (Mimics)Puppetry (Revenants)

Mythic Beast Domains

Dream (Ki'shiu)Forest (Ket'yia)Forest Sanctuary (Ket'shiu)Island Sanctuary (Naslunal)Snow (Essu)

(We'll find out what the "sanctuary" part means later. You'll have to just speculate about it for now.