Well, a new era of X-Men stories just began after the end of AvX and the premiere of All-New X-Men. That era that just ended began with Joss Whedon's Astonishing X-Men, encompassed House of M, and contained the "Messiah Complex" and "Second Coming" events, among others.
My advice, however, would to be to go even further back and read what you can find of the definitive Uncanny X-Men run written by Chris Claremont.
Actually, the mention of All New X-Men makes me wonder if it might be easier to just jump into the Marvel NOW! stuff in general. Would it be fairly easy to jump into those?
Most likely.
I've been away from Marvel since like 2005 except for Fantastic Four and I have had a really easy time jumping into the Marvel Now stuff I've read (New Avengers, Uncanny Avengers, Avengers, Indestructible Hulk, All-New X-Men).
Also there are some other Marvel sereis that aren't related to Marvel Now that are relatively new and of high quality. Daredevil is 21 or so issues in and has been downright amazing. Daredevil may be the most consistently well-written character in mainstream comics and this run is no exception. And Hawkeye, which is about to come out with issue 7 has been amazing.