How to play a "crazy" character?

For our next dnd game, I'm thinking of focusing more on role play than pure power. I'm usually the only min-mixer at the table, so I thought to try something different.

The character I'd like to play is the wise fool or mad sage archetype, someone who acts crazy and nonsensical, but beneath it all there is some deeper wisdom. Think the Ice King from Adventure Time or Kinger from Amazing Digital Circus.

Looking for some suggestions on how to best play this character without being too out of pocket or too weak (again, role-play was never my strong suit).

Also, any thoughts on the build itself would be appreciated. I was thinking a Paladin, but idk.

Thank you and wishing you all a lovely day!