The origin of the JLA was revealed in Justice League of America Vol 1 #9 when seven heroes first came together to repel the Appelliax alien invasion. When the world's greatest heroes were unable to defeat this alien threat individually, the Martian Manhunter, The Flash (Barry Allen), Green Lantern (Hal Jordan), Wonder Woman, Aquaman, Superman and the Batman cooperated together as a team to defeat the Appelliax invaders. These heroes continued to work together as the Justice League of America, after realizing they worked well together.
I'm thinking with the Justice League movie, Martain Manhunter in Mars senses an evil up rising. Darksied kills all Wonder Woman's sisters. She tries to take him out herself but fails. He says to her he's going to conqour Earth and she won't stop him. On Earth Superman is chasing lex luthor on a jet. He uses his super vision to slice his jet pack. Lex ejects but Wonder woman cacthes him and slams him to a wall.. She introduces herself to Superman telling him that a threat is comming. Superman says that he's allready taken care of every villian. So Wonder woman travles to Gotham and hears about this Batman and confronts him. Batman says he's done with super hero stuff. Wonder woman tries to reason with him and finnally Batman says yes. At Oa the Green lantens gare gathered together then Darkseid appears Many lanterns try to mstop him but fails. Hal goes to Earth. His friend Berry Allen, who has recently earned the name the Flash and tells him that they need to team up to fight this guy. Flash aggrees. Wonder Woman goes to Atlantis and finds Aquaman. She tells him that she needs his help. He aggres. Then Darkseid goes to Europe to start his plan. He starts to kill many people and he won't stop untill they Knell before him. Wonder Woman, Aguaman, Batman arive and start to beat the crap out of him. Then Hal, and flash appear. They see the three and it looks like thier helping them. Hal slams Wonder woman to the ground Flash confronts Aquaman. Darkseid escapes to the eifel tower. Super man find him there. They confront. Superman says it's been a wile since they last seen each other then They battle. Martain Manhunter stop the fight between Flash, Hal, Wonder woman, Batman, and aquaman. He sys that thi is nonsense and they let the villan run away. Superman comes in with Martain Manhunter. Wonder woman says, i thought you wouldn't help. Superman replies, I didn't think it was Darkside I'll help. The Marti says that he'll hjoin too. Now hey must work as a team. Then Darksied at Chacago relases an army called the Appelliax invaders. They see that he has released an army and they try to fight and stop it. Superman and Martain manhunter confront Darkseid. Then he's defeated and Wonder Woman closes the portal with a romote on Darkseid. Darkseid is taken care of by the Green Lanten corps. Flash says that they work together nicley and should be nammed something colorfull like the Justice League.
So that is how I think the movie should go down. But with more excitment.