Fate main series watch order:

1. Fate/Zero (2 seasons)
2. Fate/stay night 2006 (I highly recommend skipping this and watching after the other FSN animes)
3. Fate/stay night : Unlimited Blade Works Prologue aka Episode 0
4. Fate/stay night : Unlimited Blade Works (2 seasons)
5. Fate/stay night Heavens Feel (3 movies),

If you have no idea what Fate is or where to start, just watch the shows mentioned above.

Any other Fate can be watched at any time after completing the main series as they are all spinoffs.

Fate/Grand Order : (Adaptation of the mobile game - Fate no/Grand Order)

1. Fate/Grand Order : First Order
2. Fate/Grand Order : Babylonia Initium Iter (prologue ep)
3. Fate/Grand Order : Babylonia (1 season)
4. Fate/Grand Order : Shinsei Entaku Ryouiki Camelot (2 movies, second movie blu ray set to release on December 22, 2021)
5. Fate/Grand Order: Final Singularity - The Grand Temple of Time : Solomon (movie blu ray set to release on January 19, 2022)

Fate/kaleid liner : 1. Fate/kaleid liner Prisma Illya 2. Fate/kaleid liner Primsa Illya 2wei! 3. Fate/kaleid liner Prisma Illya 2wei Herz! 4. Fate/kaleid liner Prisma Illya 3rei!! 5. Fate/kaleid liner Prisma Illya : Vow in the Snow (movie) 6. Fate/kaleid liner Prisma Illya - Licht Nameless Girl (movie, no blu ray/digital release yet)

Some Other Notable Spinoffs : (These are in no specific order) 1. Fate/Apocrypha 2. Carnival Phantasm 3. Today's Menu for The Emiya Family 4. Case Files of Lord El Melloi II 5. Fate/Prototype 6. Fate/Grand Carnival 7. Fate/EXTRA : Last Encore