Zero's a prequel written by a different author from the original VN a couple years later, and right off the bat it takes the assumption that the viewer has played Heaven's Feel to completion. Unless you want to end up drowning in proper nouns, avoid watching it until you've seen all the original FSN stuff out there.
The stuff from UBW and HF I've heard gets spoiled in Deen Stay Night seems minor. Obviously the big reveal about Archer is included, but at this point it's internet folklore that everyone knows. The stuff from Heaven's Feel is pretty minimal - supposedly just visual cameos and allusions that don't actually spoil that story's big reveals.
There's a Let's Play of all three routes of the visual novel here: https://lparchive.org/Fatestay-night/