The player who controlled the creature that went to the graveyard (and caused Takklemaggot's second ability to trigger) chooses what creature Takklemaggot will return to the battlefield attached to. The creature isn't chosen until the ability resolves, so no player can respond between the time the creature is chosen and the time Takklemaggot returns to the battlefield attached to it. The ability doesn't target a creature, so a creature with shroud, for example, can be chosen. However, only a creature that can be legally enchanted by Takklemaggot can be chosen, so a creature with protection from black, for example, can't be chosen. If the player can choose a creature, they must do so, no matter who controls it. If the player can't choose a creature, Takklemaggot returns to the battlefield as a non-Aura enchantment, and that player is the player that Takklemaggot will deal damage to.