My rankings might be a little controversial but you did say best and not favorite. I ranked more on the musical side and less on the movie side. Thus a lot of movies ended up surprisingly low because of a lack of songs.
1. The Little Mermaid 2. Pocahontas 3. Beauty and the Beast 4. Anastasia
5. Hercules 6. The Hunchback of Notre Dame 7. The Princess and the Frog 8. The Nightmare Before Christmas 9. Snow White 10. Aladdin
Honorable mentions: The Prince of Egypt, The Lion King II: Simba's Pride, Thumbelina, The Swan Princess, Frozen, The Lion King, Cats Don't Dance, Barbie as the Princess and the Pauper
Of course I haven't seen every animated musical. Did anyone catch that Dorothy movie with Lea Michele?