Continuity Reboot: Technically the first installment in the new X-Men series following the Cosmic Retcon in Days Of Future Past (though First Class is still canon).
To show this trope is in full force, the writer has confirmed that we will likely see entirely different iterations of characters who appeared in the original trilogy. Word of God is that thanks to Mystique's actions in Days of Future Past, history has been altered so greatly that some mutants have now been born long before they were in the original timeline.
Foregone Conclusion: Since the movie takes place in the 1980s of the new timeline, and the ending scene of DoFP takes place later in the same timeline, it is obvious that at least Xavier, Wolverine, Beast, Rogue, Iceman, Shadowcat, Colossus, Storm, Jean and Cyclops will survive the events of the movie.
"At the end of the movie, [Magneto] flies away without his helmet, with the implication that he'll go off and continue to be Magneto in some form, but not be able to hide it from Charles, who'll be able to read his mind and track him. There's a truce of some kind between Charles and Magneto, but there's a part of Magneto that will always be the Magneto we know from the comics."
Simon Kinberg: So he's not just somebody who's out there destroying the world because he can. What he's doing is – in his mind – justified and validated by a real compelling, coherent philosophy. He tries to proselytize and convert people – maybe some of our most familiar characters – to come to his cause.
"If First Class was Erik's story and Days of Future Past is Charles' story, then Apocalypse will be both of their stories. The first movie was about Erik becoming empowered. That's the origin story of a man's power. Days of Future Past is about a guy who is a mess, masterminding the end of this massive movie. So they are both at their peak powers at the start of Apocalypse, so Apocalypse for me is the culmination of that three-act love story."
"It is a fascinating relationship. Erik grew up without a family, it's such a huge part of him, of his mission. So the idea of exploring what it means for Magneto to be a father and reconnect with a son many years after his birth, is fascinating and certainly something that would be interesting to explore in future films."
James McAvoy and Michael Fassbender will be 36 and 38 years old, respectively, during filming, but their characters are in their late forties/early fifties in 1983.
Nicholas Hoult will be 25 years old, but if we assume that his character was around 20 in 1962, then in 1983 Beast is pushing 40.
Time Abyss: Since he was young during the reign of the Egyptian Empire, En Sabah Nur has been around for four to five thousand years at the least.
Time-Shifted Actor: It has been confirmed that new actors will portray the teenage incarnations of Cyclops, Storm, and Jean Grey. In addition, an older actor will play the older incarnation of Apocalypse.
The Quest: In the last film, Wolverine asked the younger Xavier to find Jean Grey, Cyclops, and Storm as soon as possible. The search for these three will be part of the main plot.