You can't actually wipe out the Jedi or Sith 100%. Even if you killed all of them both have Spirits, holocrons etc floating around.
Yes and no. If you go strictly movie canon, there's no such thing as a holocron mentioned, IIRC. And (barring the current one I haven't seen yet) the only spirits mentioned in the movies are Qui Gon, Obi Wan, Anakin, and Yoda, and it'd be super-easy to have them only speak to the Skywalker bloodline, and so be silent for your PCs.
I played Saga Edition for a while, and had some outstanding stories. We did it in an alternate past of the Jedi Civil War (so, about 5000 years before the movies), so far back that nothing you're going to do will impact the on-screen canon. IN our version of things, the Jedi managed to stop Revan and his Sith forces, but at great cost. The Jedi were all but obliterated, and the Old Republic lost trust in the Jedi, and the Temple on Coruscant was closed.
With one exception, the PCs all started as non-Jedi, but were expected to multiclass into Jedi as the game went on. We were a bunch of force sensitive people found by one rather flawed Jedi Knight. Not even a master himself, the tragedies he'd seen led him to try probing the future... rather too much. He was convinced the ultimate fate of the Order lay in us, so he gathered us up and tried to teach us.
It was messy.