You choose the target artifact or enchantment card in your graveyard as you put the triggered ability on the stack. Once the ability starts resolving, you choose which creature card to exile from your graveyard, if any. At that point, no one can respond to your choice or take any actions until the ability is finished resolving.

If you choose an artifact creature card or an enchantment creature card in your graveyard as the target, you could exile that card as the triggered ability is resolving, but if you do, you won’t return it to your hand.