If a permanent has more than one of the affected types, it can count for any of them. For example, you could choose an artifact creature as the artifact you're sparing, another creature as the creature, and an enchantment creature as the enchantment. Similarly, you could choose an enchantment creature as both the creature and the enchantment that you're sparing, even if the player controls another creature and/or another enchantment.

None of the chosen permanents are targets of Tragic Arrogance.