There are essentially two things that make a Star Wars game...well, a Star Wars game - your light saber and your force powers. Both of these abilities are handled well in Jedi Academy and give you ample chances to make your Jaden custom.
You start out with a basic set of force abilities. The eight starter powers you will start with are saber offense, saber defence, saber throw, sense, jump, speed, pull, and push. From there you have eight more powers to choose from. Four of them are labeled light side and the rest are labeled the dark side. You can buy these powers, each of which you earn at the end of each mission. Just be warned - you can not buy out all of the powers. You will have to choose between specializing in a few very strong powers or having low levels of all of them.
Your light sabers are a different deal. You start out with a standard saber. Later the choices expand allowing you to use dual light sabers or a light saber staff aka Episode One. In addition you have a choice of stances. Your main choices are basically between a slow and strong stance or a fast and weak stance. You also have some choice in color as well, but this is just cosmetic.