The First Order - After RotJ, they started as an imperial remnant that withdrew to the Uncharted Region and allied with Snoke, a Dark Side user from the planet Ren, who was head of a cult that served Palpatine. The First Order is not a 'new empire,' though. Rather, they have a base of operations, and then recruit people from around the galaxy with offers of power, and are methodically overthrowing planets by trying to foil efforts of the New Republic to keep the peace, and in turn claim that only the First Order can restore the security that the empire provided. In a way, they're a bit like the Islamic State.
Also, they've been gradually kidnapping and brainwashing children to be their soldiers, and those who are found to be force sensitive are trained to be the Knights of Ren.
Ben's Backstory - Luke tried to train some new Jedi, Snoke manipulates Ben Solo, and the Knights of Ren came and destroyed the temple. (Ben should've been a young teen at this point - this would've been maybe 15 years before TFA).
Ben knows that when he leaves, Luke will come follow, and that Snoke intends to kill Luke. So Ben hacks Luke's X-Wing to take him to some random planet and strand him there. Snoke sees this as a mark of weakness, and wants to find and kill Skywalker, but Ben honestly doesn't know where he sent Luke. He just let the Force be his guide.
Ben joins the Knights of Ren, and adopts the name Kylo Ren. He's the strongest Force-sensitive in the group, and travels to Endor to recover his grandfather's khyber crystal from his funeral pyre. There he had a vision (which we'll only learn of later), seeing the Force spirit of Anakin Skywalker. Anakin warned him that Snoke is but a minion of the Sith, and that he can sense the spirit of the emperor still persists. It is gathering power to be reborn. Snoke never reveals where his master is, so Ben decides to embrace the Dark Side, to earn Snoke's trust, and then to finish what Anakin started: the defeat of the Sith.
Rey's Backstory - Her parents were no one famous, true. However, they're not scum. The First Order came to Jakku about fifteen years ago. Rey's dad had been a Rebel pilot, and his mother a Rebel spy, who after the Empire fell, Luke realized were both Force sensitive and offered to teach them. But they declined, wanting instead to return home and raise a family. After Luke was exiled, the First Order tracked them down. Afraid for their daughter, and with few options in an emergency, they sold her Unkar Plutt, moments before they were captured and carried away.
Han and Leia Backstory - Their relationship fell apart after Ben disappeared. They hadn't heard about him for years after he joined Snoke, and while 'Kylo Ren' has become infamous, they only just realize that it's him during TFA.
Leia has been trying to warn the New Republic about the First Order. At the start of TFA, there's not any coordinated Resistance yet.
Han and Chewie aren't smugglers; they're on a mission to stop this ship of monsters from being taken to some villain or other, but they detoured when they detected the Falcon.
Finn and Poe and Rose don't need any changes.