I'm flattered (though I sort thought this would be the obvious story for Brainiac...no?)
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Anyways, perhaps these are the roles/dynamic every member can have, with regards to Brainiac:
Superman: The reason why Brainiac had an eye on Earth in the first place, being from Krypton, aware of Kal El's escape. He possesses knowledge of Krypton's demise, etc, using this knowledge to try to get Supes off his game. Supes is convinced that its his fault, his responsibility, he's hesitant about drawing other people into the conflict, etc.
Batman: An intellectual game. Bats has to try to outsmart a supercomputer. He puts together the plan, using each member's specific abilities to infiltrate Brainiac's ship. Although he's the 'loner', he's the one who suggests putting the squad together to Supes.
MMH: A former victim of Braniac's forces, who destroyed the Martian society. He's the one who possesses knowledge of Brainiac. (perhaps Brainiac's 'green-form' is inspired by the Martians)
GL: The one who failed to protect Mars. A lot of tension between him and MMH. Feels a sense of indirect revenge against Brainiac.
Flash: The reason why Brainiac came to Earth, revealed in a twist at the end. He wants to find/capture the Flash (which isn't easy to do) to learn the ability to travel through time, perhaps to "learn the truth" (about the origins of everything, tying into the Old/New Gods intrigue)
WW: The one who commands the Amazons, free from Brainiac's reach. (an invisible ship also serves as a handy make-shift base of operations during their recruitment/mission; free from the global surveillance of Brainiac)
Aquaman: The one who commands the Atlanteans, free from Braniac's reach. (perhaps one of these societies should refuse to help)
(or Cyborg: The one who can combat/infiltrate Brainiac's network, perhaps without being detected.
If he's not in this one, perhaps some remnant of Brainiac's technology can give way to Cyborg in a future movie)