So, now that we have established how Mutants can exist in a world without them, let's see who would be in the first film. Remember, the X-Men did exist but they were disbanded, so the story could be about them forming the 'band' again.
Now the hard part of any X-Men film, which members to include. For this, I'd have to start with those who have had little to no story in the Fox X-Men movies so they can be done right this time. So sadly, no Wolverine for now.

I believe the best members for the X-Men to pull from would be:
Storm - She has been the leader of the X-Men from time to time and I really think Fox has underutilized her. In this I imagine she went back to her African kingdom to rule as it's Queen/ Goddess, like she is in the comics.
Beast - I think Beast has not only been underutilized but not done justice. I imagine Beast being done like the Hulk or Rocket, a CGI character because in the comics he is most well known for looking like this . /m…, and let's face it, that can't and hasn't been done by using practical effects. I think he would be hunkered down in the ruins of the X-Mansion (much like Winston from Overwatch).
Nightcrawler - Kurt was very good in X2, then they forgot him, and the Apocalypse one was just for laughs and that's not the character. I imagine him being more like the version form Wolverine and the X-Men, going around helping mutants who are being mistreated.
Psylocke - The badass ninja mutant was one of the pluses of Apocalypse, though she was also underutilized and given no backstory, just 'we need a fourth horseman, how about her, people like her, we could make some profit with her'. I think she'd be in Britain trying to hunt down those who switched her body.
Jubilee - Though I could have easily placed Iceman here as the jokester of the team, Jubilee has been done nothing within the Fox movies. I think she can work in this though, and she could very easily be the POV character.
Gambit - The Cajun thief was meant to have his own movie, but unfortunately we may never see him again. So, this time we'll see him at his best. He'd be a good replacement for Wolverine as the darker hero, probably found fighting off the Assassin guild.

Who would be playing them can be seen here: watch?v=Ivo9wI…

So now that we have a list of heroes it's time for villains. Now, yes Magneto will be in it but I feel he shouldn't be the first villain. Play him up to be a very dangerous man, have him be the Emperor from Star Wars for the X-Men. So, instead we'll have a smaller group from his army:
Mystique - Now yes, Mystique has been heavily done in the Fox movies, but I think they went in the wrong direction with her. Why is she suddenly the main character of the franchise? Instead let's go with a more comic book accurate version (especially with the costume, something like this /wp-content/up) She would be a very high ranking warrior for Magneto, carrying out an important mission.
Madrox - I think he could work. Not only would the special effects of him using his powers be cheap so the studio can put more effort on other characters, but try imagining an army of Madrox fighting against the X-Men.
Domino - Again, very easy to show and cheap on the effects, though the makeup would need to be perfect.
Blink - Now I know Blink was a good addition to DoFP, but what most don't know is that she actually had lines that were cut from the film. And this usually wouldn't be a big enough issue, as many characters in the film didn't get lines, but her actor was not fluent in English and had to learn it for her lines...and then they take them out of the final cut. Not cool guys, not cool.
Toad - I think Ray Parks could do the role again, and Toad was really good in the first movie. Add some modern special effects and you've got a very dangerous mutant, especially if Ray Parks plays the role (he's Darth Maul if you didn't know)
Rogue - Now for the southern belle. I believe that for this she should be starting off as a villain, like in the comics and becomes a hero later on. And since Captain Marvel would be existing alongside her we can finally see her to her full potential; flying, being super strong and bulletproof.

Next we will get to see what the story will be.