Now, this is a very common thing in the anime community. Where to start with Fate?

And the answer to that question is, you can literally start anywhere. Fate Stay/Night and Fate Grand/Order aren't really connected story wise and have different continuities.

Fate/ Stay Night was originally a visual that had 3 routes. One for Saber being the 2006 anime, Rin's route being Unlimited Blade Works and Sakura's route, Heaven's Feel which is now split into 3 movies.

Fate/Apocrypha is set in a parallel world to Stay Night.

Fate/Extra shares the events set in the same universe as Stay Night, before being split into it's own universe.

Fate/Kaleid is just a magical girl spin-off of Stay Night.

Fate/Zero is the prequel to Stay Night, however if you only watched Unlimited Blade Works, you will be spoiled on character relationships in both the Saber route and Heaven's Feel.

Fate/Grand Order has a movie titled First Order that'll help set things up for the Babylonia anime.

Now it's completely up to you where to start with the series. Honestly I'm still kinda new-ish, but hopefully this does help.