I'm Country so the story comes first. No story no need for the song. So lyrics first.
Verse structure next, i.e. 4 line or 5, rhyme or not.
Chord progression next - First draft will be in C as I'll use the keyboard for the melody (all white keys).
Next is fitting the lyrics and verse structure together. Getting the chord change words to match up. Most of the time the chord progression used in the first verse follows in the other verses and more than likely in the Chorus as well. Up to this point I'm composing with my acoustic guitar.
Melody is based upon chord tones and/or pentatonic notes. Melody is worked out on the keyboard - with a number 2 pencil and a big eraser, I might add. What chord tone or pentatonic note sounds right with each lyric word.
That gets the first draft in a lead sheet format.