Oh ok. I'm not able to have my character join the Jedi Order and she left anyway to go into hiding for her niece, but now she needs a faction and I'm not sure where to put her.
The Accord is a Pro-Republic indie faction, the Bounty Hunter's Guild and Ha'rangir's Chosen are neutral and The Exchange are more Pro-Sith. All are the most active indie factions.
Gray Jedi do not work with current rules about the Force, so the Gray Jedi are mostly Jedi who act not on the will of the Council, but do not harness both light and dark side powers