I suppose I always hear the lyrics first. it started with Buddy Holly
for me;
Drunk man, street car
Foot slip,(drum rim shot)
There you are.....
Well I'm looking for someone to love..

probably the most succinct piece of lyric writing in popular music. It's a film, a book, a play...
"Strollin", my friend, as you know Sonny Curtis wrote "More than I can say". I worked with him once and when I got back to the dressing room he asked me who'd written a song I sang.
"I did, Sonny"
"Fine song man." he said.
It's never got better than that!
I got into songwriting through the tradition as I heard it, ie the telling of stories with music, and that's still what I listen for, although it's harder to find these days in the welter of "me" writers who don't have much of a story to tell.
it's interesting. looking back, that I was the first person in the world to record a Paul Simon song except Paul. It was "Most peculiar man" a direct piece of storytelling, and not one of his more "poetic" lyrics. Then I heard Harry Chapin....but that's another story