Ground Zero's does a good job of filling you in on the story. Phantom Pain just continues it. You can play it without having prior knowledge of the other games.
There is a chronological order to the series despite the games having numbered 1 to 4 they do not follow in chronological order.
Phantom Pain is supposed to be the final game in the series that brings the story together and helps millions of players understand the connections all of the characters have with each other.
I saw it as I logged into Reddit! It looks so awesome!





