Uncanny X-Men by Claremont: Basically the run that put the X-Men on the map as one of the biggest franchises in superhero comics, let alone Marvel.
New X-Men by Morrison: Ridiculous and over the top, but like Claremont's run, it's essentially a reboot of the X-books that felt like a "restructuring" of sorts. Showing the X-Men in a completely different light.
All-New X-Men[/B] by Bendis: Another restructuring of sorts for the X-line after Avengers vs. X-Men. Combining this with Bendis' Uncanny X-Men creates a really great run of X-books.
Those are the runs that I feel are best for a complete beginner with zero X-Men knowledge. There are a few books that I think are still great, but I think work best with some already working knowledge (though that's not necessary).
Astonishing X-Men by Whedon and Cassaday: My 100% absolute favorite superhero run, comic run, and X-Men run of all time. Extremely great characterizations, plotting, and dialogue, all while paying great homage to the X-Men's history. Fantastically drawn by Cassaday. Following Morrison's New X-Men directly with this creates a pretty great X-story (especially because Whedon draws from that as well as Claremont's run).
X-Men by Mike Carey; Again, fantastic character work and plotting while digging deep into the X-Men lore. Like, deep. Immensely rewarding to longtime X-fans whilst still accessibly to newbies.
Uncanny X-Force by Rick Remender: A fantastically dark story dealing heavily with the nature of heroism, sacrifice, and murder. Remender knows his shit and applies it well. Again, benefits more from having some sense of the mythos, but not necessary. It's perfectly standalone, but pulls from an area of X-Men lore that I never gave a fuck about until this run.
Those are the ones I can reasonably recommend. There are other good X-books to read, but those are what I can reasonably recommend to a newbie.
Can probably also throw up Ultimate X-Men as well, since the Ultimate books in general were designed for beginners. I recall reading the first few Ultimate arcs and enjoying them a lot. It's been awhile and I do mean to revisit it.