On the other hand, when auditioning for American Idol, the best strategy is to pick a really well known, "All American" song that the audience and judges will identify with. Again, you should be yourself and sing it your way, not simply copying the artist.
For any competition, when choosing your song, it is also important to choose a song that fits you. For example, if you have the range of Johnny Cash, don't choose a Mariah Carey Song, and vice versa. If you have a solid southern accent, rap is not going to be your best pick for competition. Also, if you look and move like William Hung, probably don't choose a Ricky Martin song unless you are going for laughs of course!