Uncanny X-Men by Kieron Gillen (let's lean into his hotness with fans at the moment, eh?)
(UXM #526-544, 534.1 & Ann3, UXM #1-20, Heroic Age: X-Men, X-Men: Regenesis, Generation Hope #1-12, Steve Rogers: Super Soldier Annual 1, Namor Annual 1. I'm not sure you could squeeze in AvX: Consequences. You don't actually need Schism to understand what's happening here, especially with the GenHope Schism issues.)
X-Men by Mike Carey, Vol. 1
(X-Men #188-204 & Annual 1, Secret Invasion: X-Men #1-4, X-Men Legacy #208-225, Wolverine: Origins #28-30, X-Men Original Sin, and maybe material from X-Men: Pixies and Demons - Director's Cut (2008), X-Men: Divided We Stand (2008) #1-2, and X-Men: Manifest Destiny (2008) #1-5. Most X-books break best around Second Coming, but this book has a better break with Rogue gaining control of her powers.)
X-Men by Mike Carey, Vol. 2
(#226-234, 238-260, Giant-Size X-Men Legacy, Age of X: Alpha, New Mutants #22-24, and Age of X: Universe #1-2 - yes, I'd include the pair of Utopia issues and the Necrosha issues, they work fine on their own. We could also pad this with X-Men Origins: Beast (2008), X-Men Origins: Gambit (2009), Wolverine: Firebreak (2008), and X-Men: No More Humans OHC)
PS: I'll be back with a more refined look at this plus A LOT MORE X-Men omni suggestions later this week, so no need to hurry up and vote