I have plenty of experience using Linux on the desktop (Damn Small Linux, Puppy Linux, Ubuntu, Linux Mint, and antiX Linux), but I have NO experience whatsoever with servers.

I'd like to set up my own server at home on a second computer and learn how to do basic things (mail server, web server, firewall, etc.). Some questions:
1. What distro do you recommend and why? I've read great things about Debian's stability and lightweight operation. I've tried Debian on the desktop, and what I didn't like was the LONG installation process that reminded me of Windows.
2. What books and web pages do you recommend for getting started?

I use Ubuntu for build servers and test servers. If you use the server install you will get a very small initial install. Then you can use aptitude from the command line to install anything you want to add.

Debian would be a good choice. It is very stable, easy to maintain, and there is a lot of documentation available for Debian (or one of it's spin-offs) server configuration. I personally use Slackware on servers as I like the simplicity of BSD-style init over the SysV style used in Debian (and pretty much every other Linux distro, for that matter), but it is not as easy to maintain.

As for books, I am sure there are many excellent books about Linux server administration, I don't personally have any of them. I learned as I went, and made use of online resources like LQ. I am sure somebody else could suggest a modern, comprehensive, book that you could start with.