I think that the About section on LinkedIn can give the most important introduction about you, your experience and communication skills. It's basically a summary about you that either make people interested to know more or move on.
Do you have some examples that are clear, innovative, eloquent, interesting, etc.?
Not necessarily LinkedIn, any other similar thing is acceptable.
It's hard to say, and it depends on who you are. I believe that links to your work are better than some marketing slogans. I mean something like:
- Creator of example.com
- Invented MyFramework framework https://github.com/user/myframework
- Blogger at https://medium.com/user
etc.