Ok, here's my shot at a good story:
Movie starts with Mystique, in the shape of the 1974 Stryker, driving up to a mansion and bringing a casket sized chamber, made of glass, filled with fluid and with Wolverine inside, unconsious, on an automated lift, inside. She is shown entering into a laboratory type room, where she leaves the body. She enters through a doorway into a study type room. A tall figure is standing with his back to her.
"I have brought you what you asked for".
The figure replies "You have done well, Raven".
He turns. It's Nathaniel Essex.
Raven says something about the deal. Discussion between them reveals that she is doing this in order to free a bunch of mutants (as we've seen her motivated to do in DOFP).
It then reads across the screen, "Ten years later"...
At Xavier's School for Gifted Students, in the Danger Room. Beast is in the control booth watching the action. Cyclops, Marvel Girl (both around 18 or 19 years old) and Quicksilver (mid-20's) are standing in the middle of a large, circular room with technology all around (obviously the Danger Room to those who know).
Beast says "Alright, let's see what you've got", pressing the buttons and dials to get the Danger Room to run through a Savage Land (jungle) scenario.
They are in the middle of a field, surrounded by thick trees and vegetation, when they become attacked from mutliple directions by a group of velociraptors (could be Man-Apes, or some other Savage Land creature type to give the nod). Cyclops is taking out one here, and one there using his optic blasts. Marvel Girl is using her telekenesis to pick one up and throw it into another. Quicksilver is standing there nonchalant, almost bored, doing nothing to help. Cyclops, realizing that they can't keep up with the number of creatures attacking them says "Pietro, want to help here?"
Pietro replies "If I must...". He speeds up and starts running through the horde of creatures, similarly to what he did in DOFP, moving the velociraptor's legs and placing stones and logs under their claws, all the while dodging Scott's slow-moving optic blast and the hovering creature that Jean is tossing telekenetically. He comes to stop back in his starting position next to Scott and Jean. Time resumes and the entire horde of creatures all crash in a tangle of bodies and stones and logs, etc.
"Too easy." Quicksilver says, matter of factly.
Suddenly, from the other side of the field, a huge creature, red in color, that is easily recognized as a T-Rex, bursts through the tress, stampeding right at the trio. Scott fires his optic blasts, but the creature is too large and they bounce off it's tough hide. Jean puts up a telekenetic shield, which slows the huge beast, but just barely. It takes all of her concentration to keep it up.
Quicksilver is about to go into action when a screech from behind causes him to turn. A huge pterodactyl is on him, it's claw clamping onto his shoulder like a vise and pulling him from his feet as it flys away. Pietro thrashes, to no avail. He tries to use his powers, but that ends up causing him to just shake violently.
Cyclops raises his head towards the flying lizard, but realizing the danger states "I don't have a clear shot". With things quickly getting out of control, his leadership skills take over.
"Jean, when I say, drop your shield."
He raises his hand to the side of his visor, adjusting a knob to it's maximum rotation.
"Now!"
Jean shuts down her telekenesis as Scott sends out a huge concussive blast. The creature is defeated and crashes to the ground in a cloud of dust.
"Jean, use your telekenesis to hold that thing".
Jean does as she's told, stopping the creature from flying away, but unable to bring it to the ground as she fights against the force of it's wings.
Once again, Scott raises his hand to the side of his visor and adjusts the knob in the opposite direction. He takes careful aim and fires a very precise shot at the pterodactyl, killing it instantly. It, and Pietro, plummet towards the ground. Jean reaches out with her mind, grabs Pietro, and guides his body to them.
The scene around them changes back to the Danger Room as Beast enters from a door that comes out to a mezzanine, around 20 feet up on the wall. He somersaults down to the kids and rushes over asking "How bad is he hurt?"
"I'm fine!" replies Quicksilver, rubbing his shoulder.
"Debriefing in Professor X's study in 10 minutes"
We then see Professor X sitting in his wheelchair using Cerebro. We are brought into his mind as he reaches out searching for something. We are shown the globe as he focuses on Europe. His mind zeroes in on the sole red figure in that area as we are brought in. We see the figure and he says "Mein Gott".
Professor X takes off the helmet, showing his finally bald head (pay McAvoy extra) and smiles.
CAIRO, EGYPT
On the streets of Egypt we see a man in his mid-20's walking through the market. When we see it is Channing Tatum (wearing street clothes - not Gambit's uniform) it becomes very obvious that this is Remy Lebeau. A situation occurs where a young, dark-skinned girl, around 18 years old, with white-hair, bumps into him and appoligizes. He instinctively places his hand to his back pocket and realizes his wallet was just taken. He turns and see the white-haired girl disappear around a corner. He takes off in pursuit. As the chase ensues he ends up grabbing a pole from a vendor's cart. At a certain point, when he sees the girl turn right around a corner, instead of following he goes a different way.
We then see the girl, believing she has escaped and is alone, checking the contents of the wallet. Suddenly the man drops down from the roof of the building behind the young thief holding the pole. He says "Nice try chere'. And ta think I now needs to be a thief of my own wallet".
The young girl tries to run for it, heading towards a small hole in the side of the wall of an obviously vacant building across the alley. Gambit's eyes flash purple as he charges the pole and tosses it ahead of the escaping thief. The wall explodes, crumbling in a heap blocking her escape. The girl falls back and the wallet lands at Gambit's feet.
Ororo: "How did you...?"
Gambit picks up his wallet, pulls out some money, which he hands to the young girl.
"Here, dis for you. My names Remy, some call me Gambit. An I know what you're t'inkin', ma petite. Dat Gambit... he sure is de suave one, no?"
Gambit walks away...
(Going forward, let me just surmise the story)
Back at the mansion, in Professor X's study. They hold some conversation about the Danger Room simulation. The discussion, of course, leads to some life lessons about arrogance (Quicksilver), trusting your powers (Marvel Girl) and leadership (Cyclops). Some discussion can take place about how well the new ruby quartz visor worked, which was created for Cyclops by Beast, and maybe how realistic the Danger Room is.
Professor X then informs them that he has located another mutant and that they will be leaving immediately.
This is when we'll get into Mystique and Magneto. Mystique has formed a Brotherhood of Mutants that includes Toad, Ink and some others. Maybe Avalanche and Destiny are part of this group. This force is going up against some government installation where a mutant is being held. Maybe Destiny is the mutant that they are trying to free. The battle happens and in the end Magneto saves them and brings them to his lair, which is within a moutain.
Back to the X-Men who are flying on the new Blackbird. Maybe Hank is teaching Scott and/or Jean to fly. Quicksilver is either sleeping, or having a conversation with Professor X, possibly about his father (and sister?). Anyway, they arrive, stealthily land and go to this European circus. They get to see the Amazing Nightcrawler's trapeeze act while Professor X goes to talk with the gypsy foster mother of this Nightcrawler's. During their talk we get to see the past where a beautiful woman is carrying a blue-skinned baby, which she ends up leaving to be found by a younger version of this gypsy woman. From the yellow eyes of the woman as she tearfully turns away from her baby the audience knows it's Mystique.
We then see Mystique, and her Brotherhood, with Erik as he talks about the past ten years and his isolation. Mystique wants him to fight to protect the mutants, but he has come to the conclusion that there can never be peace. Maybe Destiny confirms that mutants and humans will never truly be able to live in harmony. There can also be some discussion about Azazel with the implication being that Mystique developed feelings for him after he left them. After all of the discussion Erik states "I have come to a decision and would invite you to come with me", or something like that.
Back at the circus the kids are watching Nightcrawler do some amazing things. A situation happens where a child is in danger and kurt displays his teleportation powers in order to save her. The audience is awed and scared. This all leads to Kurt leaving with the Professor and the others.
Back in Egypt it is now night and we see Gambit dressed in his costume, bo-staff in hand. We see him approaching one of the Pyramids of Giza, going up and out of sight. He pulls out some sort of key and uses it in a keyhole that would be almost impossible to find. We see Ororo watching steathily a little ways off. Gambit enters through the stone stairs that were uncovered when he used the key.
We then see Gambit deep down in the heart of the pyramid, entering into a huge anti-chamber. He walks up to the dais in the center of the chamber and ascends the steps. He pulls out some sort of energy source and puts it into what appears to be alien technology. The blue energy from the power source travels around the technology as it powers up. Four smaller sarcoghaguses light up and four figures emerge, as Gambit descends and backs away. This could be a place where Gambit gains access and takes a piece of this technology. The main sarcoghagus then powers up and out comes Apocalypse.
Back on the Blackbird, Professor X (and maybe Jean as well) feel the massive disturbance caused by the awakening of Apocalypse. Professor X guides Beast to Egypt.
Back in the pyramid, the being stands and says "I am En Sabur Nur, the Apocalypse, and I have come!" (or something like that - as if we would need to be told). Some dialog might happen between Gambit and Apocalypse (or his Horsemen). Maybe something about him being sent to awaken him. Suddenly Ororo, who obviously followed, appears at the doorway. Apocalypse tells his Horsemen to kill her. Remy reacts and uses his powers to bring down some of the ceiling on top of one of the Horsemen. He runs, taking Ororo with him.
The remaining Horsemen give chase. Remy's powers cause a cave-in trapping Ororo near the exit, Remy outside, separated. Suddenly the skies light up with an electrical storm. The hair on Remy's arms lift due to the static. Remy can hear Ororo screaming on the other side, when suddenly a bolt of lightning strikes the place where the debris from the avalanche is.
The Blackbird appears and Professor X mentally communicates with Remy, who is craddling the unconscious Ororo. A battle ensues between the three Horsemen and the X-Men (and Gambit). This is the first time we get to see Nightcrawler use his powers in battle (what are some good ways to have his powers combine with the others?). Ororo is not doing well so they hasten their escape.
Back at the mansion Ororo is being cared for, with Gambit never leaving her side. She comes to, introductions, etc.
Sinister and Apocalypse are then shown together, maybe at Sinister's lab. Sinister is definitely subserviant. Apocalypse needs a new Horseman Death. Sinister unveils Wolverine. Wolverine either already has his adamantium back, or we get to see him go through the process. Maybe Apocalypse does something to Logan's mind, making him into his Horseman.
I think it would be neat to see them use real life experiences from 1983, as they have in the other movies. One that could work is the marine barracks in Beirut. Maybe it's Apocalypse's Horsemen who attacked the military installation. Wolverine can be made out, by those that would know him, as one of the attackers. We get to see Ronald Reagan call this a "dispicable act".
The X-Men see this all on tv and Professor X and Beast recognize Wolverine. We get more dialog and interactions among the X-Men.
Erik and Mystique show up at the mansion. Erik explains that he is leaving and explains how he will create Asteroid M. Mystique is not going to go and she tells Charles et al about Essex and how she gave him Wolverine. She needs to help fix this. Erik drops the bomb that he is Pietro's father. Pietro decides to leave with Erik (he has daddy issues).
In preparing for the battle this would be the time to get into Mystique and Kurt, if that can be included in this story. This could be part of Mystique's redemption.
We get to see Magneto, along with Pietro and other mutants, create Asteroid M.
Back on earth, the team's go up against the Horsemen and ultimately win, though Wolverine/Death got away. This is where we could see Nightcrawler wielding a sword. Jean (or Professor X) was able to psionically determine where Apocalypse is and information about the celestial technology.
They go after Apocalypse. Working together, they battle. They remove Apocalypse's celestial armor, making him vulnerable. Someone (probably Ink) needs to die. Some how they get through to Wolverine, waking him up, so he can fight as well. Apocalypse is ultimately, by all appearance, defeated.
After the battle, Mystique and her Brotherhood take their dead and leave. She still has work to do.
Back at the mansion Professor X is helping/talking with Logan. Not going into the future discussions with him, just about the mansion, what they do, etc. Everyone else is just hanging, enjoying each other's company, etc.
After credit scene: Sinister reforms Apocalypse's body and puts him into a regneration chamber. Maybe Remy appears and they hold a dialog about how that didn't go very well. Remy gives to Sinister the thing he stole from Apocalypse's pyramid back towards the beginning of the movie, setting up another movie...