Basically there are team champs like supports and tanks and than there are other champs that you still need the team but you won't be punished because you know that if someone doesn't help you it won't mean too much.
Gives No Lux1 votesIf you want to be a team player then IMO the best solo queue champs are those that save your teammates from the stupid things they do. Heavy CC, peel and shields namely.
Lux, Mao and Lulu will get you pretty far and they're pretty easy to pick up. Annie, Ori, Zilean, Rammus, Naut are also good on their own and for the team.
If you want to be an island than any split pusher and just /mute all and push all game.
