The triggered ability will resolve before the enchantment spell that caused it to trigger.
When you cast an Aura spell, you have to choose a target for it before this ability puts an Angel token onto the battlefield. In other words, you can't play an Aura spell intending to enchant the Angel that will be created as a result.
Casting Sigil of the Empty Throne won't trigger its own ability. It has to be on the battlefield for its ability to work.