Aaaa. I loved Fate/Zero too. x3
Fate/Stay Night is the sequel, but it’s horrible compared to Fate/Zero. Don’t watch it.
(It’s basically Shirou Emiya and his pack of magical girls trying to fight off bad guys. It turned into a harem. </3)
You won’t miss anything except some minor background info needed for Carnival Phantasm (some parody of various Type Moon shows).