For those with Nvidia cards; I've been having all these issues listed above myself as I have a GTX 660 Ti, which is one of the cards that currently has issues running FFXIV:ARR. Black screens, major FPS dips and client crashes gallore... I've taken a bold step though and downloaded the recently released 326.80 beta drivers from Nvidia and even though the black screens still occur, it does not drop my FPS afterwards. I also haven't had any client crashes yet since I've installed these drivers. But I've only had it installed for a few hours, so I might've just been lucky. But either way, in case you want to risk running a beta driver, you could give driver version 326.80 a shot and see if that fixes some issues.
My guess is that Nvidia is working on a certified WHQL version that does support FFXIV:ARR, but I highly doubt we'll see it released within the early access period. And if not, I really hope SE fixes their client to properly work with the affected Nvidia and AMD cards soon.