I think it really depends on what you are like, there are alot of different ways to read about Dharma.
The book that did it for me is Cutting Through Spiritual Materialism by Trungpa Rinpoche, while it is not a structured book on Buddhist teaching exactly, for me it really got to the heart of things, and I feel like reading it gave me a perspective by which I could judge the appropriateness of other material for myself, and eventually pick out a Sangha etc., for me it really helped frame and clarify the entire question of what I was interested in Buddhism in the first place. Meditation in Action is also wonderful and deals if I recall with a bit more structure in terms of what Buddhist concepts it covers.
So that's a my pick on a personal level, but really I think they are not great picks for many new people. Truly the TNH book covers all the "basics" in a plain-language way, with some really excellent analogies I haven't seen before, which is not what Cutting Through does at all really..so it depends on what kind of message appeals to someone. I am a loud weirdo coming from a certain point of view, I am more attracted to "crazy wisdom" than I am to the quieter, more stoic-seeming flavor of Buddhist expression.. so what speaks to me may not be what speaks to others, I also tend towards "big picture" stuff rather than well-organized discourses.
Honestly for introductory stuff there is also alot of good material available online if you are willing to search, Buddhanet's e-library for instance has a bunch of PDF's that are great.http://www.buddhanet.net/ebooks.htm
I've also heard great things about DPR's book, though haven't read it myself.
"Just as a lotus does not grow out of a well-levelled soil but from the mire, in the same way the awakening mind
is not born in the hearts of disciples in whom the moisture of attachment has dried up. It grows instead in the hearts of ordinary sentient beings who possess in full the fetters of bondage." -Se Chilbu Choki Gyaltsen