>>6259451>>6259457In the best case scenario you should play the VN the guy linked, the route order is Fate>Unlimited Blade Works>Heaven's Feel and I'm pretty sure the game doesn't let you start the routes out of order anyway.
If you don't feel like reading the anime order is Fate/Stay Night Unlimited Blade Works TV by ufotable>Fate/Zero(this is what I usually recommend but nothing's stopping you from starting with Fate/Zero). Skip Fate/Stay Night and Fate/UBW by studio DEEN or watch it later. You're free to explore the franchise after that, when it comes to anime there's Fate/Apocrypha which has some great characters that sadly don't get developed nearly as much as the awful characters but it's fun sometimes.
Fate/Extra Last Encore is just fucking weird man and I wouldn't recommend it to someone not familiar with the Extra universe spinoffs and even then it's a mindfuck.
Prisma Illya is good if you don't mind the loli fanservice. Great worldbuilding and characters with quite a few nods to the original.
Heaven's Feel is worth watching but only the first part out of three is out and it will take several years till it's done
>>6259554Visual Novel is the source material. It's just more extensive. Often stuff like internal monologues aren't adapted into the anime because it'd become a boring slog