Melody, lyrics, music for listening. The melody sets the emotion of the song. Thats the part that's going to grab me or not. Then the lyrics. I'm picky. If they are not thoughtful lyrics, they can turn me off the whole song. By music, I assume you mean the song, the whole enchilada? That (for me) is a higher level appreciation of how the parts are joined, seqeued, etc. ...But I don't know if I got your meaning right.
FWIW, when writing, it's usually storyline and general lyrics first. I'm big on meaning, and the lyrics can change to suit the melody. However, I usually have one melody to start. Usually the chorus. The verses are easy if they are a logical storyline. I suck at bridges. They are the bane of my existence :D
...so ever since then, I always hang on to the buckle.