You can't really presume what genre a teenager would like based on a set of personality traits. What a person likes musically is influenced by far more than their personality. Your character will almost certainly enjoy at least some of the music their parents listen to regularly, music enjoyed by older siblings and/or the "cool" aunty and uncle, old stuff they listened to during weekend visits to Grandma's that get them a little nostalgic after she died. Music listened to by their social group, whoever that may be. Music they have access to.
Speaking on behalf of my once teenaged rebellious troubled outcast other half, he liked;
80s and 90s rock, but not the really heavy screamy stuff. Unless the drumming was really good or the bass line cool in which case he enjoyed it despite the screamy voices. Or sometimes the screamy voices would work in the context of the song. And his dad's collection of music including the Pixies, David Byrne, Brian Eno, Talking Heads, Foetus. And classical music. And he loved movie soundtracks to movies he enjoyed, regardless of the genre of the song, including the cinematic music made just to back scenes in the film. And 80s montage music. And 80s pop in general, but not the songs that were all empowerment and shit. And Queen because seriously, who doesn't like Queen? And proper 70s punk because it was the only stuff he could convinvingly sing to after his previously angelic boyish singing voice cracked. And he loved, LOVED, Screaming Jay Hawkins. And Big Mama Thornton. And the bleepy, boopy soundtracks to the Amiga games he played. Especially the Lemmings theme. He still puts that on now, in fact.
His tastes haven't changed really, but they have widened. No one in his family ever really listened to pop music or watched shows like Top of the Pops or had MTV type channels on their TV. It was mostly radio 2. So he'd never heard a lot of the more everyday bands that I loved like Eels, Skunk Anansi, Babylon Zoo, etc. When he heard them through me, he greatly enjoyed them.
He can't stand Oasis. He can't quite articulate why.
One thing that has changed; kids now can access even more obscure and unusual music through youtube etc. My 16 year old cousin has an ipod stocked with, in addition to an eclectic range of music, the nomnomnom song, badgermushroomsnake, Tim Minchin's pope son, You are a Pirate, Nyancat...