Yes....both.
In addition to getting your points, you can learn how to compete. Tournaments and leagues can teach you different things. The pace of tournaments is slow and tedious, learning patience and how to stay in the game, is a lesson here. Leagues can be very distracting. Players are not as focused and there are a lot of outside static, that you might not find in tournaments. Just a couple examples. Many players are glad to teach and help you along the way, enjoy the chances to listen and learn.
Oh...your points. Pick a couple larger tournaments and play AM3, if your rating allows.
Have fun. Learning how to become a good tournament player is about a lot more than score. You only spend a few minutes each tournament actually throwing, learning to love and enjoy the rest of the round, is the trick.