Blue Knight
Water Spirit
Towns Folk
I admit playing like other characters would be really fun and interesting, but not doing Link's dungeons, maybe their own side stories to flesh them out :3There should be DLC where you can play as a different character/and their story (like Zelda or Impa). It does get pretty boring being Link over and over. I think it would be really interesting exploring dungeons/landscapes, using their own unique abilities/weapons/attacks on bosses and enemies. They could collect gems/medals or something else from dungeons to progress further. The final boss could be their eternal rival (not Ganondorf). xD
As for rivals... I don't think the series would benefit from giving a rival character to Link y'know? It has always been kinda like, either an ally or a complete enemy kind of deal, and Link, Zelda and Ganondorf have been the big power players, with the rest being minor antagonists or allies.