Wow, she actually has really good tastes for someone so young! I wouldn't be concerned about her music taste at all. Sure, some of the rock is "rebellious", but that's a common ingredient found in a lot of rock and roll music--past and present. She's young and probably just going through emotional changes like every girl and boy goes through while growing up. You, too, I'm sure, went through many emotional changes and phases while growing up, though your changes might have been slightly different. From clothes and styles, to friends, to hobbies-- everybody goes through them. It's how we all figure out who we really are and that might be what she is doing. Instead of thinking of this as a negative thing, embrace her and who she is as a person. Take a positive interest in her and be happy that she's trying to find her inner self, not to mention take an interest in something.
I, like your daughter, liked this sort of music at her age and never did it have a negative affect on me or my future. I liked the music. It made things happening in my life make sense. Music can be very soothing, whether it be a waltz played by a symphony to a metal band screaming their lungs out. Some music might not seem too "wholesome" or "peaceful", but it helps one release certain emotions and feelings inside which can be a good thing. It's just music and I'm sure she's a great girl and will continue to be.
On another note, not liking rap or Twilight isn't a bad thing. In fact, it shows that she can make her own decisions, which is independence. Independence is usually taken as "rebellion" to many parents and you need to tell the difference-- which I know is hard at times seeing as there is a fine line between them. As far as style goes, I didn't read anything that suggested she dresses "scary" or inappropriate. Many people dress that way and wear those colors on a daily basis. Rap, on the other hand, can have negative lyrics that are sexually suggestive and violent--so, her not listening to rap shouldn't be taken negatively. She's not swayed by cultural phenomenon's and can think for herself. She demonstrates personal strength by not "jumping on the bandwagon" and from what you've described, she seems to be a normal and intelligent teen who has matured wonderfully.
There is nothing wrong with "being different" or "not the norm". Being different does not mean "being a bad person". Take pride that your daughter is independent. Though she might not ever say it, your acceptance of her as a person means the world to her and you need to show her that. Acceptance communicates love and understanding, which is what you need to do on your part and show her.
In conclusion, snooping on your daughter will most likely cause tension between you two which is definitely not a good step in the right direction for your relationship with her. If you let her be independent and show some trust in her, she will most likely respect you more and your relationship will be healthier as a whole.