While I like the idea of a Wolverine-less "traditional" X-Men movie, I fail to see exactly what will seperate this type of film from X-Men 1 except for a slight changing of cast/roster...
I mean, who are the X-Men going to fight? Magneto and the Brotherhood, right? So that'd be...what? Mystique (again), Toad (again), Sabretooth (I find that unlikely)...and who are the X-Men going to be? Cyclops...Jean...Storm...a young Beast, that's all that's different. What's the plot? Magneto wants to replace humanity...but Xavier and Magneto seemed to establish that they would be at odds/war with each other in X-Men 1, rather than indicating that they'd battled all-out previously ("Magneto believes that a war is brewing...", "Magneto's right, a war is coming...", unless you want to retroactively read this reference to war as the battle in X-Men: The Last Stand).
However, I'd still enjoy it, so here's an idea:
Scott, Jean, Storm and Hank are the young X-Men, as established. Scott's arc is either a) that he's trying to live up to the responsibilities he faces as a leader, or b) that he is trying to put words to his feelings for Jean, or even c) both. Jean is struggling to contain the power the dwells inside her, scenes with Xavier (hinted at in X-Men: The Last Stand) will serve to indicate her constantly on the verge of losing control of herself. Storm should be darker, harsher, being out of her element from being worshipped as a Goddess and surrounded by people who now hate and fear her. Hank should be the oldest, the straight, thinking man, who has an out-of-character moment where he loses control and gets mad, possibly at Magneto/in some plot relvant way (like revealing some secret.location or something) so he can have some guilt issues to give him a dramatic arc.
The Brotherhood should be comprised of Magneto (here in a less active, mentor-like role and "Man Behind The Man" position to be seen as a more specific dark mirror of Xavier), Mystique (covert operations, as per usual, but serving as a mirror to Storm's hatred of humanity to help her work out her issues a bit to accept her new family in the X-Men, but not forgive humanity yet beause that "happens" in X2), Avalanche (a mirror for Cyclops; an arrogant prick who has no problem in trying it on with Jean and overlooking Scott completely), Toad (a snarky little bugger who eggs on Beast, contasting Beast's power with his speed and being a bit dimmer where Beast is smart), and...how about Quicksilver? Haven't seen him before, and he's Magneto's son. He can be sly and cunning and maybe try to tempt Jean into joining the Brotherhood (I admit I was struggling for a fourth member, so any other ideas are just as good, but it should be someone to contrast Jean a bit).
I think an interesting plot element could be using Havoc in some capacity as well, perhaps he joins the Brotherhood and causes some angst between him and Scott, only to convert back. If not him, then at least one member of the Brotherhood should join Xavier's school and convert to good by the end. I was gonna suggest Avalanche, but I see him as being such a prick that it might be better if it was Quicksilver (or if he at least turned on Magneto and went out on his own).
I think Moira should be a presence at the school, helping Xavier to define his mission and his training, and there can be X-Kids at the school, but it'd be better to focus on the "First Class" entirely and showcase them as a team, but also a sbickering adolescents.
As for plot though...I suppose Magneto would send his Brotherhood out to attack (I hesitate to say "kill") certain key members of the government in acts of terrorism to try to bully the normals into accepting Mutant superiority, or at least recognising Mutant rights. This, however, hurts Mutant negotiations more than it helps, as Mutants are perceived as a threat to national security and the public. This damages the fledging X-Men, who have been attempting to do good as a superhero team (by the way: no X-Jet in this film) and are now feared for being a similar terrorist group. This leads to an inevitable confrontation between them and the Brotherhood, in two conflicts in the streets (a conflict of physicality, insults, and manipulations) before the final fight at the end.
However, this is a smokescreen for Magneto's larger plan, which is to place Mystique inside Washington to impersonate key members of the senate to obtain valuable information...of some sort...which, alerts Xavier to Magneto being the Man Behind The Man and leads him to confront him in a meeting that either does, or does not, cost Xavier his use of his legs.
This is where I'm fizzling out of ideas, but I think the film should obviously take place after X-Men Origins: Wolverine, but should not show any footage from that film, only refrence the rescue of Scott and the others. I would rather not see a whole bunch of MUtant cameos, just leave them in the background and focus on the four-on-four rivalry with the X-Men and the Brotherhood and the personal issues of the X-Men. With no Wolverine, you can argue that most movie-only-fans will be put off by his absence, and it's hard to argue against including him somehow. But for the sake of continuity, I say don't; don't even hint at him past the reference to that rescue.
The film should end with Beast (he could be human looking, or furry....maybe even transform as an effect of his temper outburst mentioned earlier, either due to science (!) or a surge of Mutation) leaving for Washington or to begin a career outside of the school, and the X-Men established as a team (and Scott and Jean as a couple) with the unveiling of the X-Jet, flying off on another mission (but not out to save Rogue and Wolverine to tie into X-Men 1, these X-Men will still be to young for that). If you absolutely must work in a Wolverine cameo, it should be something really subtle, like an airport scene when he steps off a plane (from Japan, perhaps after the events of Wolverine 2) and has to take cover from a battle between the X-Men and the Brotherhood (but it is important that he shouldn't actually see any of the Mutants).
Much as I like Wolverine, and the X-Men, I would love to see a more team-orientated film, but there's so many issues surrounding it that I'd be surprised if it was done. Or done well.