Card types that can be exiled from a graveyard include artifact, creature, enchantment, land, planeswalker, instant, and sorcery. Legendary, basic, and snow are supertypes, not card types. Human, Equipment, and Aura are subtypes, not card types.

Cemetery Illuminator's ability allows you to cast a spell that shares a card type with the exiled card, even if the card on top of the library doesn't. For example, if you've exiled an artifact card, you could cast The Omenkeel from the top of your library, even though it's the back face of the modal double-faced card Cosima, God of the Voyage, which isn't an artifact.