As topic says, Fate/Zero and Fate/stay ... I know they are connected to each other, and I know Fate/Zero takes place 10 years before Stay

But I have no idea which I need to watch first

Stay has been made 6 years before Zero, but does that change something?
Or are they so much different that I can watch them in any order or what?

Please, lend me your knowledge on this one!

watch fate/stay first, then fate/zero even thought chronologically it's reversed. If you watch it reversed, a lot of events in fate/stay will be spoiled for you and you'll hate the animation quality.
after that watch fate ubw movie