For emotional songs it's just Cruel Angel Thesis for me. I was surprised but happy no one picked it. Youthful, melancholic and hopeful feelings all at the same time for me when I hear it.
https://www.youtube.com/watch?v=k8ozVkIkr-g For cute characters I'll pick Kaolla Suu from Love Hina. Cause Edward was taken and it was a tie for me anyway.
First pic is just from the anime but it's a fitting representation. I like Kaolla/Ed's happy-go-lucky vibes when set in a fantasy world. You can do anything, the world is yours to explore, those sort of vibes. I think it works well for a cute character especially when they are competent when neccessary.