Well, since I'm fairly new and not yet in any official factions, I'll just say what my ideal faction would be like.
Firstly, a nice friendly, welcoming atmosphere.
Secondly, shared ships, not only for the leaders, but for everyone. I don't really want to be forced into playing a low ranking fighter pilot all the time. I want to play a variety of roles, from a light interceptor, to a gunboat captain, to an admiral.
I want the chance to fly a cruiser, without risking all of my own credits on a ship I either don't like or can't play well. I want to be given the opportunity to be an admiral for a day, and to be given training and advice on how role-play that character to a high standard.
I would like the Admin team to subsidise group ships to better enable the advancement of a wider range of role-playing.
I want to be trained both in combat and in role-play. To train individual skills and group tactics, and how to better interact with other players.
I want to be part of a group where everyone having fun is the top priority.
By the way, if your group is already like that I've described, why don't you contact me?