There are three different paths you can take to become the top fighter. It is advised that you do not try and tackle more than one at a time as you will not have enough time to recover between fights.
Rookie League
This is the first fight circuit you will be able to join and works using a ranking system which is determined whether you win or lose. You will not earn any money in this league until you get near the top.
Ultimate Fights
Once you have unlocked these by talking to the man at the Abandoned Warhouse you will be able to earn money by fighting instead of working. The downside though is if you get injured during a fight you will reduce your training effectiveness.
Street Fights
This path becomes unlocked the first night you go out with Roy.