The Big Three for Kingdom Hearts

[Koh]

To be honest, you only have to play the other ones to get certain plot points, but what stopped other gamers from playing some games out of order? You're free to play KH3 without playing any of the side games.

Not so sure about that. It's like this in terms of story....

Birth By Sleep impacts the story a LOT; it explains the reasons why things are they way they are. Then comes KH1, and we get the whole thing versus the Heartless. Then comes 358/2 Days which talks about Roxas' time in Organization XIII (sort of negligible; I've never played this game and still understand why things are the way they are in the story). Next Chain of Memories in which Sora first meets Organization XIII. Following, KH2 for the battle against the Nobodies. Then ReCoded (totally negligible; adds a very miniscule amount of story), and finally Dream Drop Distance (Picks up after ReCoded, and impacts the story a LOT.)

If you can't play the games, it'd do you well to at least watch their cutscenes.