Here are a couple of clips I found on Youtube from MTI where Sondheim himself discusses how to interpret and play the songs. He gives insight on major themes that permeate the score, further the plot, and develop character.
https://www.youtube.com/watch?v=psk5KyE7MOg - The 6-note bean theme that's present in Jack's song to Milky White, the beginning of "Stay With Me", and "Giants in the Sky"
https://www.youtube.com/watch?v=9AfHZlofGU4 - "Hello, Little Girl" as a two-piece contrasting song with vaudeville themes that allows delineation of Red's easygoing nature and the Wolf's mysterious, predatory character
https://www.youtube.com/watch?v=iGQlbaITD5E - How the intentions of the opening prologue begin from the first note in "Once upon a time...", the "marching" staccato beat signifying characters walking towards the woods, etc.
The whole 52 minute video is here: https://www.youtube.com/watch?v=NUN_MTChn5M
This is for those who insist that Sondheim intentionally leaves the score for Into the Woods vague and dismisses his overt intentions as "subjective declarations" of fanboys. He knew what he was doing and everything had a clear purpose.
I personally don't care about anyone's opinions regarding Phantom's score, and don't have any strong ones myself, but just thought these links might help clear things up.