If you exile an Aura with Brago's last ability, the Aura's owner chooses what it will enchant as it comes back onto the battlefield. An Aura put onto the battlefield this way doesn't target anything (so it could be attached to a permanent with shroud, for example), but the Aura's enchant ability restricts what it can be attached to. The Aura can't enter the battlefield enchanting a permanent that enters the battlefield at the same time. If the Aura can't legally be attached to anything, it remains exiled.