The Dragoon 30-50 storyline establishes the lore of the Azure Dragoon. It establishes Alberic and his successor, Estinien. Playing through HW as a Dragoon feels thematically right, as you knew Estinien for longer and knew his struggles.

The 50-60 Red Mage storyline gives you more lore on the revolution. If you play SB as a Red Mage, then it can feel like you're the disciple of a fallen order, returning to set things right.

Samurai doesn't have much to do with Stormblood. The connection is tenuous at best. I thought that (60-70 spoilers)
[spoiler]The student of Musosai's who turned evil would be Zenos, but it turns out to be just another NPC[/spoiler]. The only real parallel here is that Zenos wields a katana too.

The Dark Knight story doesn't really have anything to do with the story of Shadowbringers. They are only aesthetically similar.