Though the music is important, it should never over-power the natural sounds and dialogue that are part of the scene. Those are primary to the story and must be maintained at all times, even at the cost of hearing appropriate music clearly. The best way to do this is to integrate the music, and then lower the volume right as the sounds and voices in the scene become the focus. You do not have to worry too much about drowning out the background sound unless it is crucial for establishing the mood and location of the scene. Music with words should try and be avoided when possible, unless those words serve a purpose to the film beyond their simple lyrical content. If the song is classic and recognizable it is likely that the audience will not try and make out the words and the song can still be used to define the mood. If it is an original or lesser known song you may want to avoid lyrics while people are talking on the screen. Even when no dialogue is happening, if you can hear the lyrics they better correlate to the scene either situationally or emotionally otherwise they will seem obtuse and useless.