My team:
I wanted to keep a classic team but still have some fresh faces and diversity, I think it makes things way more interesting than having everyone have similar backgrounds.
Superman, Batman, Wonder Woman and Flash are no-brainers for me.
Cyborg was also an easy choice, he adds a lot to the team with his abilities and tech, plus his dynamic with Shazam brings some youthness to the team like Wally and Kyle's used to.
I added Mera because I think it's long past time she joined the team.
Shazam is there to bounce off of Cyborg and for the naiveté and connection to magic.
Zatanna would finally rejoin the team as the only one actually capable of manipulating the mystic energies. She also has kind of an edgier personality than a lot of the team, which would be cool to explore.
Vixen is another character I feel belongs on the premier team, she's just awesome and a I think she would make for a great spokesperson.
I also wanted a Green Lantern, but I think Power Ring adds a new dynamic and Hal is usually too busy to join the team these days and I'd want John on a more cosmic oriented JL team lead by Martian Manhunter.
Lastly, I'd add Element Woman. She has so much untapped potential and I don't think we've really seen her past explored. I'd portray her as a transgendered woman with a real positive outlook on life. Her powers might make her look different, but she'd feel incredibly blessed to have them. I think it would be cool to have an LGBT on the League, the team is usually pretty conservative but adding a transgendered woman and members like the new version of Zatanna could change things up a little.
I know the team would be pretty big, but all 12 would only be together on the biggest battles. On smaller missions, they'd rotate 7 members for each mission.