Best/favorite/most influential Hans Christian Andersen stories?

I was planning to read some Hans Christian Andersen, and opted to start with a few random stories. I tried The Flax, The Fir Tree, and The Daisy, and haven't really cared for any of those three, so I thought I'd focus on stories that are more specifically influential or considered his best, such as The Little Mermaid or The Snow Queen. So, what are his best,most influential, or just your favorite of his stories?