Welcome to Eorzea!
As well as echoing the above (especially Moose's "don't take this as true unless there is proof to back it up", something that I admit I have been guilty of in the past - posting a theory that I thought had proper proof but was more just something I had misremembered!), are you also new to the FF series itself? The reason I ask is FFXIV, including it's story, features references, callbacks and allusions to all the FF games that came before it, along with references to a number of spinoff and non-FF SE titles, so you would be likely to miss many of these clever fanservice references if you're unaware of the games that FFXIV is alluding to. Each FF game has a unique setting, characters and story though so don't worry if you haven't played like FFVII and feel you're 'missed out' on understanding FFXIV's story!
The only previous title that really has a deeper connection to the current FFXIV story and setting is the original version of FFXIV, version 1.0, that has been shut down, and which ARR is a sequel of story wise - you do not have to know anything about the events of FFXIV 1.0 to appreciate and understand FFXIV ARR's story though, as the revelant info is covered in ARR.
Hence, the FF Wiki is probably the best place to start with getting your feet wet about the FF series in general and all the titles that FFXIV refefences if you're unfamiliar with the FF series at large. Although I agree with Obsidian above about avoiding it's specific FFXIV pages, as there are few things there that are wrong (mostly the page on the Echo involves a misconception of how it works and how it helps the player, which I won't go into here), the rest of the site, and the pages for FFXIV 1.0 at least, are fine.
And this is the FFXIV forum thread where players have tried listing all the known references and allusions to past FF games (many of which are not on the FF Wiki's own listing!), naturally this is a work in progress so there is bound to be a lot that still lies buried!
Anyway, welcome once again to Eorzea! (And the lore forum!).