I got annoyed trying to decide on the composition of my parties without good reference documents, so I decided to write some up. This is simply a table of classes, their two skill trees, the equipment they can use based on those skill trees, and how to unlock each class. The later sections also list which skill trees can use (or are prohibited from using) each type of equipment, as well as a list of classes (and subclasses/specializations) by skill tree.

There will be some exceptions, especially among artifacts and relics, and light armors seem to often have exceptions, but these categories should generally be correct.

I hope it's helpful!

Equipment that all classes can use aren't listed here. Classes that can use Heavy armor can also use Medium & (non-chest) Light armors; classes that can use Medium armor can also use (non-chest) Light armors. See the later sections for more info.

Heavy Armor: Battle & Retribution
Medium Armor: Archery, Battle, Blades, Nature, Retribution
Light Chest Armor: Arcana, Divine, Sorcery; not Battle
Light Armor, other: All (mostly; some exceptions)

Strength weapons (melee, physical):
Daggers (1h): Blades, Arcana - Daggers scale with both Strength & Dexterity.
Maces (1h): not Sorcery
Swords (1h): not Divine
Axes (1h): Battle, Nature; not Divine
Greataxes (2h): Battle, Nature; not Divine
Polearms (2h): Battle, Nature; not Divine - Polearms have +1 range
Greatswords (2h): Battle; not Divine
Sledges (2h): Battle, Retribution

Dexterity weapons (ranged, missile, physical):
Bows (2h): Archery, Trickery
Crossbows (2h): Archery, Battle, Trickery - Crossbows deal more damage than bows but carry a quickness penalty.

Intellect weapons (ranged, missile, magic):
Scepters (1h): Arcana, Sorcery; not Battle
Staffs (2h): Arcana, Sorcery; not Battle

Accessories (back slot):
Bandoliers: Trickery - Bandoliers increase your max power.
Battle Standards: Command - Battle Standards make enemies more likely to attack you.
Quivers: Archery - Quivers increase quickness.
Cloaks: All

Offhands (only useable if you aren't using a 2h weapon):
Small Shields: Not Arcana, not Sorcery
Large Shields: Battle, Retribution
Parrying Daggers: Battle, Blades - Parrying Daggers increase your weapon damage.
Censers: Divine, Retribution
Orbs: Arcana, Sorcery
Skulls: Arcana, Sorcery
Tomes: Arcana, Divine, Sorcery
Candelabras: All
Charms: All
Fetishes: All
Lanterns: All

And of course, everyone can use Rings.