First thing is first, for PLD you require two Battledance Materia III melded with the scimitar.

Second, I am a first time FFXIV player on a non-legacy server. I've hit 50 and have this quest now but have encountered a problem. I have had no indication or direction to The Wanderer's Palace, nor do I have any such thing in my duty finder. Is there some kind of quest that you have to get to in order to unlock this? I am to the point where I can do Ifrit (hard) and Amdapor Keep (from GC). What am I missing here?