The reference distribution for this book, and my preferred distribution, is Debian GNU/Linux, the Linux for the GNU Generation.
I originally started with Slackware in the early 90's but migrated through Red Hat and then quickly on to Debian in 1995. Red Hat is a good distribution and is quite popular but has limitations. Debian conforms to the open and distributed development model making it a very open distribution where even you can make a change to it if you so desired. Debian is the basis of a number of commercial distributions and it also powers quite a few web sites including Linux.com.
Distributions involving Debian GNU/Linux are listed at http://www.debian.org/misc/children-distros and include:
Related distributions include Amirix (http://www.amirixlinux.com/), Embedded Debian (http://www.emdebian.org/), TimeSys for real time GNU/Linux (http://timesys.com/) and the VA Linux Systems, O'Reilly and SGI collaboration (http://www.oreilly.com/catalog/debian/index.html).