The greatest barrier to entry into the Fate franchise is the fandom. That’s a common enough complaint, as anime fans are no strangers to toxic communities that pride themselves on making their favorite series far off unattainable trophies, unapproachable by the layman. The question of “what order should I watch Fate in” is usually met with a dozen different answers and disparaging the other eleven.
[the following will contain moderate spoilers for Fate/Zero, Fate/stay night (2006), and Fate/Stay Night: Unlimited Blade Works]

The second biggest barrier is the Fate franchise itself, particularly the adaptations of the first visual novel, Fate/stay night. Visual novels, for the uninitiated, are exactly what they sound like. A novel with graphic elements displaying characters and scenes, usually with the interactive elements of video games. Fate/stay night has three routes, depending on who the player romances as the protagonist, Shiro Emiya.
As this is meant to serve as a jumping on point for Fate, a plot summary is in order. Fate details the Holy Grail Wars, where seven mages summon seven historical or mythological spirits in order to battle for the Grail, an omnipotent wish granting device. Fate/stay night follows Shiro Emiya who summons the servant Saber, King Arthur, who in the Fate universe is a hot anime girl because of course she is. Fate/Zero is the prequel series, depicting the Grail War ten years prior to the series, led by Shiro’s adopted father Kitsurugi.
The first route, called Fate, is where Shiro romances his servant Saber, was adapted in the first anime by Studio Deen, simply called Fate/stay night. The second, called Unlimited Blade Works, comes as a result of Shiro choosing his fellow master Rin Tohsaka, and was made into the anime of the same name by Ufotable in 2014. Ufotable had taken the reins of the franchise when they adapted Fate/Zero in 2011. The final route, Heaven’s Feel, where Shiro picks Rin’s sister Sakura, was adapted into a trilogy of movies that finished in 2020.
Thus, with four different anime based off one visual novel and so many spin-offs, where does one begin? And, for the sake of argument, I will be ignoring the option of playing the visual novel. It would be great if everyone could spare hundreds of hours to play each individual route, but if the game suffers from an availability problem, and I generally try to avoid steering people towards piracy. So, I will be recommending people watch the anime only.

The most obvious answer might be to watch them in order of release. Watching Fate/stay night (2006) ought to be a good start, as the first route is considered to be the most accessible of the three. However, when looking at the older series, it has not aged very well, especially considering how well Ufotable has done with the animation quality in the later series. New anime fans looking to get into Fate might find themselves turned away by the considerably worse animation.
Then maybe start with Fate/Zero? It does a much better job of explaining the subtle nuances and character relationships that go completely ignored in Unlimited Blade Works. The start is a little slow for a first time Fate watcher, however, and the other shows explain the rules better. The main problem with Fate/Zero is that it centers on a cast of morally sketchy adults who all have deeply held convictions that cannot allow one another to coexist. Going to Fate/stay night after that will be a stark surprise, as a majority of the masters are high school students with much more immature attitudes and relationships.
Alternatively, starting with Unlimited Blade Works has the advantage of most rules of the Holy Grail War being revealed early on. It might feel better for viewers to jump right in to the main story rather than a prequel. The only issue with starting with UBW is that a lot of the details explained in Zero are lost, and contextualizing them by watching Zero later will lose most of the impact. Shiro’s relationship with Ilya is never explored, and Sakura and Rin’s being sisters is glanced at perhaps once in the whole series. These would be otherwise vital information, but they’re basically skipped over.

The action and animation of UBW is the best of any of the anime that have come so far, if you need the production values high to get into a show. Watching Heaven’s Feel first might have the best quality as a trilogy of movies, but it is also considered the most complex route. Besides, the other series are all available on your standard anime streaming services, plus Netflix and Hulu to boot. The last movie only came out a couple of months ago as of writing this, and not a lot of people want to shell out the money for Blu-Rays for a series they aren’t even into yet.
And then finally, there are the spin-offs like Fate Apocrypha or Absolute Demonic Front: Babylonia, which could be possible starting points as they don’t affect the main story. Still, spin-offs are generally made for already existing fans, so the exposition might skimp over parts that the main story couldn’t afford to. You could just be a psychopath and get into Fate by playing the mobile gacha game Fate Grand Order, if you haven’t emptied your bank account on Genshin Impact.
Fate is good, it’s very good, for the most part. I don’t think I need to make the case for this famous of a franchise, but I know how scary it can be to look at a series this big and confusing. Especially when people get this heated over whether or not you watch the dumb cartoons in the right order.
Personally, I think Fate/Zero is the least confusing route, even if it does spoil some of the most shocking moments from the other shows. You’re going to get spoiled on many of the elements of Zero if you watch stay night first, so there’s really no avoiding it either way. After you finish the main routes, check out the spin-offs and extras that interest you from there, not so hard, is it?

You’re not a worse anime fan or Fate fan because you watched it in a different way from somebody else. The only wrong way to approach Fate is to avoid it entirely because strangers on the internet say you don’t like it right. But also watch Fate/Zero the most of any series because it has the most of best boy Gilgamesh.