If you've played the original but not played Before Crisis and Crisis Core, imo, take the time to read the synopsis for each on FFwiki before April 10th.
There's references to both in the demo that suggest they're still canon, and as Kitase-san and Nomura-san expand the story and setting details in Remake, I think you'll benefit from knowing the references.
@ninemil Thanks for the heads up, I can tell that a lot of detail is going to be in FFVII:R! Love the work that Square Enix has done on it from what I could gather.