Then the original trilogy (plus Rogue One) will pick up with the Galactic Civil War, and the new trilogy (beginning with The Force Awakens) fleshes out his legacy after turning back to the light side of the force.
That method will give you a proper rundown of the story from beginning to end.
From a narrative perspective, it definitely moves in a far more linear fashion and could provide a great way in for newcomers who want to learn more about the franchise as a whole.
Opening on The Phantom Menace allows audiences to meet Darth Vader at a young age during his early years as Anakin Skywalker, and each subsequent move will follow his arc until his transformation into a Sith Lord.