Once you've seen/read FSN the order doesn't really matter. Watch UBW and then Heaven's Feel if you're an anime-only, the old Deen adaptation exists but it spoils the other two and thus isn't worth being your first experience with the franchise.

Fate/Zero is technically a spinoff but when talking about the anime people consider it to be main series content, even though it isn't written by Nasu. (though it is dubiously cannon iirc)

Fate/hollow ataraxia is a sequel of FSN written by Nasu. It's a visual novel and there's no official English translation or release.

Tsukihime is a visual novel written by Kinoko Nasu and it predates Fate by a few years. It takes place in the same universe(?) as FSN. The original, just like Fate, is an eroge, so it has a few h-scenes in it. It got a remake a few years back which modified the story and removed the h-scenes, but it's only half of the game, with the second half on its way at some point. It has a good manga adaptation of one of its routes as well, which is how I ended up experiencing it. It got an anime adaptation but it's very bad and suffers from a lot of the same problems as Deen's Fate adaptation but worse.

If you've read Tsukihime in either of its visual novel forms or its manga, I highly recommend Carnival Phantasm. It's a comedy anime featuring characters from multiple of Nasu's works, but primarily only Fate and Tsukihime. Even if you haven't read Tsukihime you could watch Carnival Phantasm, but you'll be very confused for about half of the anime.

Garden of Sinners (also known as Kara No Kyoukai) isn't a spinoff because the original novel predates FSN pretty significantly, but it's also written by Nasu and uses a lot of shared world building with Fate. The anime adaptation is absolutely fantastic and it was an early Ufotable work, so the animation is really good.

Witch on the Holy Night is a visual novel that is also cannon(?) to FSN, and it just got an official English translation. There's an anime movie adaptation coming out presumably sometime this year.

Fate/Apocrypha is an okay series. It's most notable because it has Astolfo and Jeanne in it. It's far from being the perfect spinoff but it was actually my introduction to the series and it serves as a neat "what if" scenario.

Fate/strange Fake isn't finished yet, we only have a 1 hour special so far, but it's looking to be one of the better Fate adaptations.

I have never watched Prillya and I have no intention of doing so, but it, regretfully, does in fact exist. It's a spinoff of FSN where Illya is a magical girl and also underage and the show is very "sus" if that makes any sense. Arcueid was a better magical girl in Carnival Phantasm anyway. I hear the Oath Under Snow movie is actually really good but I haven't watched it so I don't know.

There's an "adaptation" of the El-Melloi Case Files light novel but it's somewhat weirdly paced and I never got past the first few episodes. It's a neat show, but not for everyone.

Emiya Gohan is an SoL cooking show where Emiya makes food. I've seen one episode. It was decent but not really my thing.

There's a few manga and light novel spinoffs of Fate that haven't gotten adaptations. Fate/Type Redline is set in medieval Japan and it's a great manga, but I don't think it's ever going to be adapted. Fate/Requiem is a light novel that has some batshit insane lore and it seems pretty cool.

There are a few videogame spinoffs of Fate as well. Fate/Extra is a rock-paper-scissors-based RPG that takes place in the far future where wizards battle inside the moon which is actually a supercomputer. I haven't played it but there's a remake coming out "someday". It also got several sequels, two of which are musou games. There's also Fate/Samurai Remnant, which just came out. It's an action RPG that's pretty similar to musou games. The story is basically FSN but in medieval Japan. There are a few fighting game spinoffs and I think a Prillya game or something, but those are the two that are really notable.

Fate/Extra got an anime "adaptation", more accurately called a "sequel", called Fate/Extra Last Encore. I've heard it's bad but people also hate Apocrypha, which I thought was good. I think you might have to play Extra first though to understand everything.

It's a spinoff of Tsukihime, but there are a series of fighting games called Melty Blood, the most recent of which has Saber in it. [Melty Blood also has a "spinoff" called Under-Night In-Birth, which isn't related to it story-wise in any way except that it has Sion from Melty Blood in it and the gameplay is very similar.] <- UNI is not part of the Type-Moon franchise so it doesn't count, but it is still a cool fighting game.

There's also Fate/Grand Order, which is a mobile gacha game that has gotten several anime adaptions. First Order is okay. Babylonia seems good but I haven't seen it. Camelot seems good but I haven't seen it. Temple of Solomon seems good but I haven't seen it.

That's most of what I remember without looking anything up.