Select a song that showcases your full range and allows you to exhibit emotions and personality. You may only get one opportunity to sing, so make an immediate impression on the judges.
Choose one that enables you to hit the "money notes" right away. If you sing something that takes awhile to build up, the judges may cut you off before they see what you can do. Start with the chorus or the bridge if you prefer.
Stand out from the crowd with an unusual song choice. Over the course of the show's history, the judges have probably heard "Unchained Melody" and "I Will Always Love You" hundreds of times. You'll need to find a balance between cliché and too obscure.
Pick something that lets you add personal flair. Turn a pop song into a country ballad, for instance. Ensure that the new version "works," however, and that your inventiveness doesn't affect your vocals or the integrity of the song.
Videotape yourself singing the songs you're considering. Perform them in front of friends and family and ask for their honest opinions. Evaluate your pitch, tone, expression, movement and articulation.