If you watch Fate/Stay Night, just be careful as there are 5 series out and here are their differences:

• Zero - takes place 10 years before FSN. Would actually suggest watching it after FSN but you can watch it before. It expands on the Grail War
• Fate/Stay Night (The OG) - Came out in 2006, the original VN had 3 “paths” and all of them ended up animated, but you had to play through them in order. This one is the base, focuses on Saber and is probably your best intro to the Fate franchise
• Unlimited Blade Works - this is the second path that focuses on Rin. There was a movie and an anime series. The movie is okay, but highly compressed. The anime has earned the nickname “Unlimited Budget Works” because of how awesome the fight scenes are animated. This one is by far my favorite
• Heaven’s Feel - this was a trio of movies that in the final path and focuses on Sakura. This one was the darkest of all the paths imo. The first movie had a good set up, second was awesome, third was just an okay landing

Of course there are a multitude of spin offs, some related, some not. Basically I like to look at them all independently with just an understanding of what the “Fate” concept is and enjoy them from there.