So, I think all of these are important. But I can see some prioritizing in my playing and running RPGs.
When my goal is game-first, I don't reach for an RPG to scratch that itch. I reach for a board or computer game - Gloomhaven, Sentinels of the Multiverse, or the like. The least satisfying RPG sessions I have ever played are ones in which my focus was on the rules of the game, and manipulating them. But in Gloomhaven, that's a highly satisfying session of play.
When I'm picking up an RPG, my priorities become mixed and varied between character and story. When I am playing, I probably lean toward character, and allow the GM to worry about the story. When I'm running the game, I lean more to story, in which the players can deal with character.
Broadly, I think of rules as the framework through which we get to character and story. I then become kind of system agnostic, on the whole - I'll play virtually any system, and find the characters and stories that system supports.