I have "the bible" and think it's a good book...But it's not one I would recommend to somebody just starting out with C++.
If there was one publisher that I found useful over the years, it would be Waite Publishing. Throughout school, I think I had about 4 of their books (C++/Perl/Java), and found them all _very_ good.
The C++ one was the best one I've ever read, as far as newbies go.
I know this doesn't have a lot to do with this topic, but if somebody were to ask me for a good starting point, I would highly recommend them go down the Java route.
When I was in college, it was all C++....and midway through, it then became Java. My first year post-college was all C/C++, and the last 1+ year has been exclusively Java...I can't tell you how impressed I've been with the language. The performance issues that have clouded Java throughout the years have really come full circle, and coding in Java _really_ does make use of Object Oriented principles.
It's an easier language to master, and there are so many similarities to C++, that I feel it to be a better stepping stone to C++. Plus, Java now has support for both OpenGL and D3D.