In my opinion (as senshin said, 5 people, 6 answer), if you are looking at the series from production release order, I'd do the following.
1) Fate/Stay Night Visual Novel
All works on Fate/Stay Night are adapted from this as
- The anime mainly follows the Fate Route
- Caster's Antagonist Role later in the anime is adapted from Unlimited Blade Works. (In Fate, she appears but is shortly killed. Her goal to prematurely summon the Grail was one of the main plots of Unlimited Blade Works).
- Sakura's attacks on Rin in their battle during Caster's Arc is adapted from Heaven's Feel.
- The Unlimited Blade Works Movie adapts the Route of the same name in the Visual Novel. However, it is more faithful to the adaptation than the original anime (I say faithful in a loose sense - you can't be faithful to a few hour long game in a movie).
In terms of which Visual Novel, Fate/Stay Night Realta Nua PC is your best bet as Realta Nua uses the same updated engine as what Fate/Hollow Ataraxia uses. Realta Nua PC is for all ages and in Japanese. There is an English Patch for it and it does add an option to view both the original H Scenes from the original Visual Novel and their Realta Nua Replacements (Shiro and Saber's Bed Scene, Rin's Contract with Shiro, Rider stealing Prana from Shiro).
2) Fate/Zero
Fate/Zero is a prequel to Fate/Stay Night. At the start of the Fate/Stay Night anime, you see Saber and Gilgamesh fight it out - this is sort of what happens in Fate/Zero (in the anime they don't fight but it may have been described in the Novel). Mainly, a lot of Fate/Zero is already revealed in Heaven's Feel like the state of the Grail, the Matou Family, and the true purpose of the wars.
Regardless of the route in Fate/Stay Night, they all start from the aftermath of Fate/Zero.
3) Any other anime
From this point, you will be well-versed on the events. As such, the anime titles will be an abridged version of what you've seen, but with more stylized fights (e.g. Archer vs. Lancer), which looks better animated in my opinion.
If you are looking at the series from chronological order, I'd do the following:
- Fate/Zero
- Fate/Stay Night (anime, if you really have to)
- Unlimited Blade Works (I'd watch Ufotable's series over Studio Deen's movie)
While you say you don't intend to read the Visual Novel, you would miss out a lot. The Visual Novel isn't constricted to screening times, as such you can get quite detailed explanations of Nasuverse terminology such as True Magic, Magecraft, The Throne of Heroes, and how it's used with the Holy Grail. A lot of these are explained in the Unlimited Blade Works and Heaven's Feel Route, The latter has yet to been release (thouygh here's an Aniplex trailer).
Also finally in Realta Nua, after seeing all 5 endings, there is -Last Episode- which is in 2 parts: the first is a review of the Fate Route, while the second part is the true conclusion to the Fate Route where 2 people fulfill the conditions to perform a Miracle. You can also see it as a conclusion to the Fate/Stay Night anime since both the anime and the Fate Route have the same ending, as such, -Last Episode- would continue on from both. The original visual novel did not have this and a separate patch to Mirror Moon's patch was required to add it in.
Outside of anime there are:
- Fate/Hollow Ataraxia (Visual Novel) - This follows the Fate Route. However, it does expect that you've played all the routes in Fate/Stay Night as it has elements that transpired in Heaven's Feel.
The state of the Matou Family's as Zouken and Shinji are terrified by Sakura now that she is the head of the family and Alter-Saber being Saber's second personality
Fate/Extra (PSP Game) - This is set outside Fate/Stay Night. in the 1970's a certain event has drained Prana from the world. There are cameo's from Fate/Stay Night like Kotomine, Taiga, Rin's Lancer and Sakura, but their roles are different and not related to the original. Also, the Rin in this title, while looking like Rin from Fate/Stay Night, is not the same Rin but a descendant of Fate/Stay Night's Rin by at least 2 generations (implied to be either mother or grandmother).
Fate/Extra CCC (PSP Game) - A split from Fate/Extra like Heaven's Feel is to Fate/Stay Night. Sakura has a much larger role which also adds Gilgamesh into the mix. However, he's not so much as an ass as he is in Fate/Stay Night (though proudly showing off his naked body in front of Elizabeth as a weapon does show he's still got that ego).
Fate/Apocrypha (Novel) - If you've watched Fate/Zero or Played the Visual Novel then you know of the 3rd Holy Grail War. Fate/Apocrypha splits from the 3rd war where the Grail was stolen from Fuyuki. In this story, there are 2 teams of Servants and a new class, Ruler, which acts as mediator over the war. Also Mordred is summoned as Saber, keeping an established tradition in Fate series: the main Saber is related to Fate/Stay Night's Saber.
There are also other Nasuverse works such as Tsukihime and Witch of the Holy Night. Carnival Phantasm is a crossover of the Nasuverse like the heroes of Fate/Stay Night and Tsukihime trying to date all their heroines at the same time and alternate formats of the Holy Grail War.