I don't compete usually, but I publicly perform quite a bit.
1. Make sure it's a song you're super familiar with… If something goes wrong, you can freestyle through it because you're so comfortable with the song.
2. Pick a song you love and feel throughout your body because it shows when you're dancing. If you are happy and feeling it, it will come across to the audience/judges.
3. A song that is super popular will please the crowd but can take away from the audience focus on your dance. If the crowd is rocking out to the song, they may be less… concentrated on your skills. I use this a lot to my advantage when I freestyle because the audience is loving the song, they tend to be more forgiving when a rogue toe goes unpointed. (Crowds love Journey- but that depends on your audience) For competition, you may want the judges FOCUSED on you and not your music.
4. Don't pick a song that is generally considered unpopular or unsuited to the competition. Make sure it meets competition requirements (if they have stipulations about vulgar language or length, for example). In one of the few comps I did do, I had points (unfairly) deducted because the judges did not like my music. –Everyone else was doing R&B and Top 40 and I did Puscifer…
In the end, just bite the bullet, pick one that meets your criteria and commit. Once you do that, it's easy to focus on your routine and move past.