If you have good songs and a real desire to make music, the next thing to do, instead of approach record companies, is to get yourself a really good manager because then it allows you to focus on your profession of being a musician. Then they can focus on the darker art of the record label and the music industry.
I like 'Goodbye My Lover' because it's a really personal song and I recorded it in my landlady's bathroom in Los Angeles. She had a piano in there and for me listening back to it, it actually sounds like the voice I hear in my head. It's so close to what I can imagine.