I recommend watching Fate/Zero then Unlimited Blade Works (2014). This is the true chronological timeline within the series.
The 3 routes you mentioned are 3 different paths that Shirou can take in his life. The anime gets its source material from the Visual Novel. The 3 routes are almost completely different (coming from someone who played the games). Unlimited Blade Works, like the name says, follows the Unlimited Blade Works route. The 2014 adaption is pretty accurate, as far as the first season goes that is. The third route, Heaven's Feel, is currently being created as a feature movie by Ufotable and Type-Moon, it will be released soon.'
As for everything excepted Fate/Zero and UBW (2014), I do not recommend watching Fate stay/night which is supposed to follow the first route, Fate, because it is not faithful to the source material. It mashes up parts of all three routes, and spoils the other routes. If you really want to watch it, play all three routes, so nothing can be spoiled, then watch it. Otherwise I don't recommend it.
Fate/Kaleid follows a completely different universe with Illya as the main character. It has great music, solid animation, and is more of a cutesy anime. It is not bad, I have watched it. I would not tell anyone who wants to watch it, not to watch it. It definitely has some incredibly bad ass moments.
There is an OVA for Fate/Prototype, but that's it. For all the other routes/variations, you'll need to play the Visual Novels. There are currently no anime adaptions for them except the one OVA for prototype.
