While spitballing all these ideas, I think it's worthwhile being realistic about the cast. While fans would be nostalgic for the original team, this forms a very small subset of the audience. Even amongst comic book readers, I don't think many started from the very first few issues. As such, this simply isn't viable from a marketability perspective. Many of the original members are neither current fan favourites nor on the active main roster (therefore, not benefitting from any cross-product synergy). Instead, popular characters such as Wolverine, Kitty, Nightcrawler, etc should be considered for the main cast from the very get go. Instead, a special episode where the show's version of the original members teaming up could serve as homage.
As for the main character, Cyclops would be a safe bet. While not topping any popularity charts, he's nonetheless generally likable and few people outright dislike the character. Alternatively, Kitty or X-23 (with a greatly altered back story sans Wolverine and as a means to not even needing him in the main cast) as the 'new recruit' and audience surrogate would be pretty workable. Plus, it would potentially draw in the female demographic.
If going with the latter, the way I imagine the first episode working would be having the main character being aware of her power but unaware of what a mutant is (as the public isn't aware such a thing exists). She misuses her power but not in a way that would cause her to be seen as 'evil' by the audience (e.g. if Kitty was a homeless teen runaway who only steals what she needs to get by, as opposed to robbing banks). She would find herself being stalked by this mysterious bald man (Prof X, obviously) who she spots appearing all over the place. The plot of the episode would revolve around a problem in her daily routine resulting in her needing to give up that life after doing some heroic deed which draws unwanted attention her way. This ends with the Professor offering her a place at his Institute.
Personally, I don't think having Prof Xavier as the main character would work. He's got too many of the answers. He's better served as a mentor and surrogate father to the main character and ensemble, akin to Giles and his relationship with Buffy and the rest of the Scooby Gang.
Also, a thought about Sentinels:
I agree that trying to feature giant, mutant-hunting robots would be cost prohibitive, not to mention cheesy, for a standard live-action TV series. As such, the show could instead intentionally deconstruct the concept since such machines would have questionable effectiveness and be too costly (due to public property damage) to operate. Instead, the giant robots would instead be disinformation designed to mislead the X-Men who set out to scuttle the initiative with a reveal at the end of the episode being that the real Sentinel Programme is a far more discreet operation consisting of human-sized robots disguised as background bystanders whose function is to identify mutants and track their activities. The fake operation providing the programme the means to first identify the X-Men.
Why robots? Hive-mind.
I think if the show was called X-Men in any way it would give the show some attention already, and then adding Charles Xavier, Beast, Cyclops, and Magneto, would bring in the crowds. And 4-5 episodes in Hank becomes blue and furry, so that would help.
Then season 2 would start with more characters joining, Wolverine, Banshee, Nightcrawler, Storm, Colossus, etc. So Season 1 would introduce things and season two would expand the world with more characters, like Buffy did with her show.
I never meant that Xavier should be the main character. Just that he would be an important character and that almost everything would effect him since he started the X-Men plan. I just didn't want him to become one of those adult characters that end up getting cut out of the show because they don't have much to do. X-Men one he was in a coma, X-Men 2 he was kindapped, X-men 3 he was killed off. In Boy Meets World the parents sort of ended up not doing anything when the kids got older, and that happens a lot of shows. They kids get older and become the focus and the parents end up leaving the show or not doing anything for the show.
So Xavier would be the mentor and team leader, he has lots of answers and plans but not all the answers. Which is something I think would be cool to show.
He originally would have meant the school to be a safe place for young mutants to learn. His vision of the future would be that the school was a school for mutants, where they could learn to use their powers in peace and quite, without fear of the outside world, and he wanted them to learn how to live in harmony with the humans. Instead his vision has not become reality, the Mansion has become the home of a mutant protective SWAT type team. Something that might have been inevitable, but something he didn't want. So the show would show that Xavier tries to be their mentor and leader and wise and all knowing, but he has doubts, and regrets, and secrets. Taking on the weight of all mutants and humans and world peace is a lot to take on.
But the show would focus on the young mutants, as a team and individually. the epsidoe where Hank becomes blue and furry would focus on him. We would have an epsidoe that would focus on Scott and Jean's 1st date. etc.
In Season 2 Wolverine being added would make him the bad boy sort of element, like when Spike became part of the team on Buffy. He is this killer and a scary person, but he also has this sadness inside him. He is a killer and the best at it, with his powers and training he seems unstoppable. He is a living weapon, but he doesn't want to be. He feels like that is all he is good for, but wants there to be more. One of the reasons he joins the school. Same reason he currently has in Wolverine's X-men comic. He doesn't want the children to have to fight or kill, maybe he sees killing as something unavoidable and sees it as his job to do it (even if he doesn't say any of this out loud).
Then Sabertooth shows up to beat up Wolverine, suddenly this scary guy is being targeted by the scarier guy, bigger, meaner, like the boogy man monster. He ends up killing Thunderbird.
They all have their own reasons for being there, changing from time to time. At first the 5 original students were there for an education, then in season 2 it different.
My idea would be all about mutants and humans. Mutants are just humans with extra powers, genetic mutations. No costumes really. And no aliens, or time traveling (sort of).
Like all shows, the cast would grow and change. Season 1: Xavier, Scott, Jean, Hank, Bobby, Warren, Magneto, (and sort of Scarlet Witch, Quicksilver, Toad, and Mastermind). Season 2: Xavier, Scott, Jean, Hank, Bobby, Warren, Wolverine, Sunfire, Storm, Banshee, Thunderbird, Nightcrawler, Colossus. And later that season Sunfire leaves, Thunderbird dies, and Kitty joins the show. Season 2 also includes, Magneto, Senator Kelly, Friends of Humanity, Sentinels. Season 3: Maybe someone from the original cast leaves. Hank maybe leaves the show, or Warren. Maybe Sunfire returns, and it would also depend on the actors too. Maybe the actor who plays Cyclops wants out. The team would grow and change through the seasons, like Buffy or Smallville or any other show.
I could go on and on. I filled up like 5 pages on my own Live action X-Men thread.