The three types of music that I would recommend (or at least the types that I especially enjoy) are rock, celtic, latin and classical. Not that I have anyhting against jazz, rap, reggae, opera, R&B or any other kinds of music but these are types that I find quite appealing.

First of all, rock. Likely the music I listen to the most. I think it appeals especially to teens because alot of the bands in the rock genre are that age or started their careers at that age and sing alot about the life and problems encountered by teens. There are different kinds of rock: soft, hard, heavy metal, punk and probably alot more. There are alot of different types of rock bands ou there so it is easy to figure out which one you enjoy the most and stick to it. But try out different types because you never know what might appeal to you and they are all quite good. I really enjoy hard rock. Groups and singers such as Linkin Park, Nickelback, A perfect Circle, Avril Lavigne, Evanescence, Staind and many many more.
                                 

The next type of music I recommend is celtic. I used to be a ballet dancer, but I found that the music was too slow. Celtic is an quick and folkish type of music that usually has strings instruments (mainly violins) and sometimes wind instruments (flute). It is great for dancing and even if you aren't a dancer, you can still enjoy it. I recommend Lord of the Dance, Nathalie McMaster's music, music off the Lord of the Rings soundtracks or just any irish music!

Latin music is also very good dance music, or even party music. It's very upbeat and always has a catchy rhythm. Latin music I recommend include Shakira, Ricky Martin, South American folk music or most music out of Central and South America.