Because of the prevalence of X-Men related media out there, and the diversity within the X-Men line, introducing someone to comics via X-Men comics is not the worst idea. The monthly titles are (still) mostly a mess, but some of the collected editions are actually rather new reader friendly.
I've been re-reading the Grant Morrison New X-Men run. The writing is evenly good throughout with some neat inversions of typical X-Men stories and a whole bunch of big ideas. Reading it again, I'm amused by how much of it has been undone in the years since it was published. This is one of the absolute best runs of comics in the last decade or so, and only Joss Whedon (Yes, that Joss Whedon) and Mike Carey have done anything to follow it up.
The run was designed to reinvent the X-Men for new readers and I think it succeeds. Look these issues up online and you will read incredibly caustic reviews by old school X-Men fans. I interpret this as a very good thing actually. I've ranted enough on here on how a lot of my problems with modern comics is how they cater too much to a loud, but increasingly small base of old school fans. To see a run of comics that does the exact opposite, it very refreshing. The fact that these 40 odd issues make up a self contained story makes them some of the most new reader friendly X-Men comics available.
The one drawback to these issues is the art. There is some stellar artwork here by Frank Quietly, John Paul Leon, and others, but a lot of art in a lot of the earlier issues was rushed to publication. No offense to the talented Igor Kordey, but his issues were very obviously completed in a short period of time. About half way through the run, Marvel editors implemented rotating artists for each arc. While I disagree with some of their choices (ugh, Marc Silvestri!), it goes a long way to cleaning up things.
I don't want to talk too much about the actual plot of these issues as I think that would ruin some of the very best surprises in the last decade of comics. Lets just say that a lot of cool stuff happens and leave it at that. This isn't the X-Men from the 1980's and thats exactly why I like it so much.