I would like to see it later in perhaps the early seventies, with Xavier showing the slightest sign of thinning on top of his head. The Vietnam war would be part of the setting, if only for a blackbird flying over jungles to "all along the watchtower".
Cain Marko would be good, I would show a young Xavier in the fifties encouraging him psychically to leave home and join the army (because he's going to reveal Raven's secret). Have him fight in the Korean war. Working in the Cyttorak power might be too weird, so I'd have him modified by Sinister, who'd be a major villain in the movie, to be the Juggernaut (perhaps with celestial tech reminiscent of Apocalypse, leaving hints for the third movie). Magneto would still be present but more of the X-men's problem in the middle of the movie, who eventually helps them out before leaving still on hostile terms.
I agree that Polaris would make a good Jean grey equivalent for the first class, they should definitely keep her green hair. Perhaps have her focus more on the electrical and light aspects of electromagnetism, so she's not identical to Magneto in how they depict her powers, but ultimately she might fight him to move something metal. In this continuity she could be the mother of Cyclops with Havok, involves their relationship but changes it to fit the film.
Keep Havok, Banshee and Beast as the experienced X-men, add Sunfire and Thunderbird, who can fill the role of Wolverine-esque badass (perhaps wielding knives like Warpath has). Classic characters as well as a bit of diversity to the X-men squad. I would go with more unique costumes in the second, a variation of the jumpsuits from the first movie but with more colour combinations and individual trimmings.
Also if the Vietnam war is going, Karma might be a good and topical addition, even if only as a student the team rescues.
If you had to meet a quota of deaths/injuries, you could Thunderbird die in the manner he died in the comics and have Banshee's throat slit so he can't talk or scream. This could allow more x-men in a sequel without the team being bloated.
Sinister could set the movies up for a third film in the late 80s (perhaps involving the soviet invasion of Afghanistan) where they stop Apocalypse. This could feature the deployment of the first films X-men squad of a teenaged Cyclops, Storm and Jean with probably Beast as well a few more mutants like Cannonball, Sunspot and Dazzler. They would move back towards the costumes of the first two films (rubber-leather sci fi paramilitary uniforms).
There you have it, a potential trilogy that spans the cold war, with classic characters and villains, while still fitting loosely enough with the first 2 movies at least.