If you are into chemicals and gunpowder weapons then the Outlaws are the faction you probably want to join. Joining the Outlaws faction though is not always as obvious as you might expect.
To start your quest on becoming a Runner the first level of Outlaws then you need to follow the Desert Vultures, this will take you to meet William.
Important Note: By starting the quests for the Outlaws will cancel any other faction quests you have for the Beserkers or Clerics. You can only be a member of one faction for one time.
To start the journey to be an Outlaw you need to find William who will be in The Fort. The quest you will receive from him Tramp Confederacy is the most important but apart from this one, there are others you must finish to gain enough favour to become a Runner. The others to complete you can find from Chloe and Mad Bob.
As you complete the quests to become an Outlaw you can ask William to see how you are doing and after he will make his decision which will give you a couple responses.
Joining the Outlaws will give you 2700XP and also receive the Runner Armour, 1 Outlaw ability point that unlocks the Outlaw Skill Tree and have access to items from their sellers in Tavar and other settlements that you did not have access to before. If you speak to William you can also start your quest to be promoted to Enforcer rank.