The recent new 52 Justice League origin or variations of the first origin story work well without going into a lot of back story.
Please don't get into a critique of the actual plotting, but a story like the battle with Darkseid where characters are introduced gradually would serve fine for a movie. Alternatively, as someone mentioned earlier, one character could serve as the point of view for the audience. Personally, if the writers were to go that route, it should be someone with whom the audience is less familiar such as Cyborg, J'onn J'onzz, or even Hawkman/woman.
Most characters don't need their origins told. The audience has a passing familiarity with the big three especially. The rest of the League has fairly straightforward powers that the viewer can figure out fairly easily.
Many of the early JL stories would introduce the characters working on their own before getting together with the team.