Just don't touch anything made by DEEN. They're not good adaptations. For those who don't know, Fate/Stay Night is a visual novel first and foremost, and honestly is best experienced in its original form, anything else is essentially cheating yourself out of the whole story. Just watching a single adaptation will just result in you missing out on literally two thirds of the actual story. Not kidding. And the visual novel makes it much easier for you to understand, well, bloody well everything.
Now, the Unlimited Blade Works adaptation, so far, is pretty great. Keep in mind that UBW covers a whole different timeline than the DEEN adaptation, so don't expect it to be a complete retread. The DEEN anime covered the most boring route of the visual novel, anyway, and for those coming from Fate/Zero, Unlimited Blade Works relates much more with the events of the prequel, especially Shirou's contrast with Kiritsugu - Shirou is not nearly as generic and cliche as you think he is, believe it or not.
But, yeah, my recommendation? Read the F/SN visual novel first, then watch Fate/Zero. F/Z has quite a few major spoilers for the original VN, unless you accept that as an inevitability of being a prequel.