There are numerous prizes available through Tournament and League play including Megalixirs, Three Stars, Spheres for the Sphere Grid, Techniques for your Blitzball players to learn and more. The most important prizes though are those which are available for Wakka including his Overdrive abilities and the Jupiter Sigil for his Celestial Weapon, the World Champion.
The prizes must be obtained in the order that they are listed.
Tournament prize for obtaining first place. There are no requirements before Attack Reels appears and you will be able to play for and win it as soon as you can play Blitzball (after the first match in Luca).
League prize for obtaining first place. You must have already obtained Attack Reels and participated in at least 250 battles. Note that if you have already started the League play (which takes 10 matches to fully complete) you will not be able to change the first place prize. Status Reels will appear as the next first place prize after you complete the partially completed League matches. If you have not started any League matches just check the Save Sphere again to cause Status Reels to appear.
Tournament prize for obtaining first place. You must have already obtained Status Reels and participated in at least 450 battles. Note: If you plan on obtaining the Jupiter Sigil next you should save your game before the final match. The Jupiter Sigil only has a 50% chance of appearing so you may wish to reset your game if it does not immediately appear.
League prize for obtaining first place. You must have already obtained Auroch Reels. Getting the Jupiter Sigil to appear can be problematic as it only has a 50% chance of appearing which means that if you have a League enabled you will have to complete all 10 games to have another shot at making the Jupiter Sigil appear as a prize. Make sure that you save on your last game before you complete either the last Tournament or League match so that you can reset your game if it does not appear.