Ahh Banjo-Kazooie.... If you ever do start playing, I'd love to watch you play. I got bored of it when I played as a kid, probably because I was a completionist and got stuck on levels where you'd rescue these cute little things (I can't even remember if those were challenges or required). I think, based on this description, that you'd like it - I dunno what the music's like because I typically mute everything to put my own tunes on, but I do believe you'd enjoy the puzzle piece collection idea, and that you can go back to previous worlds. There are also some pretty neat tricks you can learn with Kazooie once you get far enough that I honestly found cute even to just watch being done (e.g. I think there's some kinda backflip thing that was both adorable and cool as heck).

Happy playing!