I'm going to take a slightly different look at this one. Years ago, I had decided that the X-Men universe needed to hit the big red 'reset' switch, and start over from scratch. There were just too many continuity problems and it was impossible for new readers to just jump in without a convoluted history lesson.
Well, they did it with the new Unlimited series. Haven't read those.
This is how I would have done it.
One of the keys of the X-Men universe is the M'krann crystal. It literally
is the universe, and its purpose is to hold reality together. In my storyline, the crystal starts to fracture. Reality is beginning to unravel itself, and only the Phoenix force (guardian of the crystal) can save things. And the only person who can control the Phoenix force is Jean Grey.
Well, she almost does it. But she can't hold it together... the crystal shatters, and Jean searches for some bit of reality to hold onto. All she finds, is her death as the original Phoenix. With one last surge of effort, she grabs onto that...
And reality solidifies. Now, we keep the X-Men continuity up to the end of the Dark Phoenix Saga, where Jean Grey dies. From that point on, my timeline takes over.
Fast forward from the 1970's to 2003. All the characters have aged appropriately. Charles Xavier is dead, and Scott Summers (now in his early 50's) is headmaster of the school. Many of the original team are now teachers, while members of the second and third generation X-Men are Blue & Gold team, with new students preparing to step into their roles. So, here we go:
Leader/Headmaster
Cyclops
Blue Team
Wolverine
Rogue*
Gambit
Scarlet Witch
Havok
Gold Team
Nightcrawler
Shadowcat
Colossus
Psylocke*
Wolfsbane
Teachers
Storm
Forge
Beast
Iceman
Rogue Mutants*
Archangel
Cable
Banshee
Magneto
Dazzler
Villains
Apocalypse
Legion*
Sabretooth
The Hellfire Club*
- Emma Frost (aka White Queen)
- Senator Kelly
- Graydon Creed
- ?
* Some explanation here, each one in turn.
Rogue is the invulnerable, flying version that absorbed Ms. Marvel. She has since purged Ms. Marvel from her mind, but lives with the guilt over that.
Psylocke is the original 'British Betsy.'
Rogue Mutants are unaffiliated with the X-Men, but not necessarily villains. They may help one time and clash the next.
Archangel has left the X-Men to pursue mutant rights through the business world. He is building upon his own wealth and buying into companies which support mutant-rights, while funding pro-mutant organizations.
Cable is still our grizzled, telepathic, infected mutant, but he's not from the future. There was no Madelyne Pryor. Instead, Mr. Sinister tried to create his perfect mutant by mixing DNA from Jean Grey and Scott Summers. The result was impressive... a child with immense power, but a flaw: his artificial nature suffered from the basic cloning problem of rapid aging. In addition, Apocalypse didn't like the idea of his 'compatriot' creating a challenger to A's power, and infected the child with his techno-organic virus. Thus, we have Cable (without time-travel!).

He later killed Sinister, and now seeks to do the same to Apocalypse.
Banshee is acting as a mutant specialist with INTERPOL. This sometimes puts him at odds with the X-men.
Magneto has cooled quite a bit since Xavier's death, but still believes a war with mutants and ordinaries is going to happen. Of late, he's retreated to Asteroid M (in orbit at a lagrange point) to plan and prepare. No one knows exactly what he's going to do next.
Dazzler has made a name for herself, of course. She's open about her mutant powers, and uses them to enhance her concert performances. The controversy around this simply drew more people to her, to the consternation of many anti-mutant groups.
Legion is Charles Xavier's illegitimate son. He is perhaps one of the most powerful mutants on the planet... but he's insane. He suffers from an extreme form of multiple personality disorder, with each personality having access to a specific mutant power. Some personalities are peaceful, but many are dangerous, and each one has a different goal.
The Hellfire Club was last heard of when it was destroyed during the Dark Phoenix Saga. However, Emma Frost quietly rebuilt it as a secret organization again. She promotes it as a secret society bent on subjugating mutants under human rule, while using her own telepathic powers to gain the advantage in manipulating the club's members. Senator Kelly is the White King, using the influence and wealth of the club to push for harsher laws, including the Mutant Registration Act. Graydon Creed quietly funds many anti-mutant groups as the Black King, while simultaneously trying to have his father (Sabretooth) killed. (I haven't figured out who should be the Black Queen yet!)