A logo, which is the centre of a corporate identity, should be recognizable and distinctive.
Secondly, it should look nice of course. If the logo manages to tell a story, that's a beautiful, intriguing bonus. Every logo creating process is different.
Sometimes it falls down immediately, other times it's a quest. But every time the search is to find something that matches. Preferable outcome: 'the most of what you do is nice, but I like my logo much more than the rest'.