You don't really need Stay Night I suppose, but it's by far the best idea to go through Stay Night first. Stay Night establishes the setting a lot more than Zero does, as Zero pretty much jumps into the story and intensity from the get-go while Stay Night takes a much slower pace. Not to mention 90% of Saber's development takes place in Stay Night so you'll find very little reason to care about her if you're just walking into Zero, which focuses a lot more on the characters that weren't present in Stay Night.
If you REALLY hate the anime, then like TheOfficialSabuto said, play the VN. As of yet I have only played through some (near the end of the Fate route), but reportedly it's much better than the anime was. The catch is that it's incredibly long. In the Fate route alone I'm pretty sure I could've watched and rewatched the entirety of the anime with how long it is, and there are two more routes of equal or greater length. Those are supposed to be even better storywise though.
