*Inhales and exhales*
Alright so let's start with the animes. If you want to watch them in chronological order the you do is.
Fate/Zero - This is the prequel to Fate/Staynight.
Fate/Staynight - The continuation of the story but is broken down into three different "routes". These routes existed in the games but also in the anime, so it's Fate/Staynight (2006) which is the Fate route. Fate/Staynight: Unlimited Blade Works is the Unlimited Blades Route and last but not least is Fate/Staynight: Heaven's Feel. This is the last route of the timeline, but these are anime movies for Heaven's Feel.
Now Fate/Hollow Ataraxia is the next thing after, which takes place after the events of Fate/Staynight. There is an anime of it but it's suggested that you read it.
Now that ends what I call the "Main Timeline", though it actually isnt. There are other anime such as Fate/Extella: Umbral Star, Fate/Apocrypha, Fate/Kaied: Prisma Illeya , Fate/Grand Order: Absolute Demonic Front: Babylonia and alot more. These's are tied to the main plot as they each take place in their own timeline/universe, so you can watch them as standalones. There is also other shows like Carnival Phantasm and The Case Files of Lord El-Melloi II which are spin off of the show two but has some times to Fate as well. I also would tell you to download the North American version of Fate/Grand Order too as it's a free game and really nice lore etc.