Question: I've caught up with the Justice League and Justice League Unlimited TV Show. I intend to start watching the Justice League movies as well. 

What is the suggest viewing order for the [Justice League animated movies](http://en.wikipedia.org/wiki/DC_Universe_Animated_Original_Movies)?

Answer: 
The [same Wikipedia link](https://en.wikipedia.org/wiki/DC_Universe_Animated_Original_Movies#Continuities) that you mentioned also has the answer to this. Most of the films before the Justice League: The Flashpoint Paradox doesn't share any continuity. Only few do, which are: 

**Superman/Batman**
This continuity is based on the Superman/Batman story line.

* Superman/Batman: Public Enemies
* Superman/Batman: Apocalypse

**Justice League**
This continuity is based on the JLA (comic book) story lines published in 2000.

* Justice League: Crisis on Two Earths
* Justice League: Doom

**Batman: Dark Knight Universe**
This continuity is based on Frank Miller's Batman (Dark Knight Universe).

* Batman: The Dark Knight Returns – Part 1
* Batman: The Dark Knight Returns – Part 2

**Justice League: The Flashpoint Paradox** also works individually, but the ending set up a new universe similar to the comics. The film came after it severed the continuity and was called **DC Animated Movie Universe**:

This shared universe is based on The New 52 continuity.

* Justice League: The Flashpoint Paradox( End credit scene)
* Justice League: War
* Son of Batman
* Justice League: Throne of Atlantis
* Batman vs. Robin
* Batman: Bad Blood
* Justice League vs. Teen Titans
* Justice League Dark
* Teen Titans: The Judas Contract
* Suicide Squad: Hell to Pay (upcoming)

**Justice League: Gods and Monsters** This universe takes place in an alternate universe and has no connection to any of the other films

* Justice League: Gods and Monsters Chronicles (web series)
* Justice League: Gods and Monsters

Second season for Justice League: Gods and Monsters Chronicles was in works but shelved for now:

[![enter image description here](https://i.stack.imgur.com/IAfuY.png)](https://i.stack.imgur.com/IAfuY.png)

The rest of the films mentioned in that Wikipedia link are standalone and can be watched in any order.

As you might already know, there are [five Batman animated films](https://en.wikipedia.org/wiki/DC_animated_universe#Films) in the DCAU. But they sever the continuity to DCAU and the order of the rest of the DCAU [shared here](https://scifi.stackexchange.com/a/46692/6006).
Prior to *Justice League: The Flashpoint Paradox*, these films were the only ones with shared continuity:

* *Superman/Batman: Public Enemies* is followed by *Superman/Batman: Apocalypse*
* *The Dark Knight Returns Parts 1 and 2*

The other films prior to *Justice League: The Flashpoint Paradox* can be watched in any order, as they don't share continuity.

*Justice League: The Flashpoint Paradox* is the start of them building some continuity into these films, based on adapting the comic book *Flashpoint* event and their *New 52* reboot. Watch that one then *Justice League: War* as it continues the story. The next film in this story hasn't been released yet, but will be *Justice League: Throne of Atlantis*.

You can watch *Son of Batman* and *Batman: Assault on Arkham* in any order as well, just note that movies released after *The Flashpoint Paradox* will sometimes be part of the *New 52* film continuity. Also note that *Assault on Arkham* shares a universe with the *Batman Arkham* games, so if you are planning on playing those, you may want to hold off until you've played them. Specifically the 3rd one, *Arkham Origins*, as the story follows it ([source](http://www.gameinformer.com/b/news/archive/2014/05/16/batman-arkham-assault.aspx)).