Not every Class can use every type of Armor or Weapon. Generally speaking, Classes can use any Armor type that falls below their own (for instance: Hunters at level 40 or above can also use Leather and Cloth in addition to Mail if they desire):
Cloth: Priest, Mage, Warlock
Leather: Rogue, Druid, Hunter, Shaman, Monk
Mail: Warrior, Paladin, Hunter (@40), Shaman (@40)
Plate: Warrior (@40), Paladin (@40), Death Knight
Some classes can also use Shields: Warriors, Paladins, and Shaman
The weapons available to your class can be found in the General (first) Tab of your Spellbook. Hovering over Weapon Skills will show all the weapons you are able to use.