There's Ubuntu, Debian, Red Had, Fedora, Gentoo, Arch, Mint, SuSE, Slackware...
A good way to find out is to look into Distro Watch. The web site more or less keeps a monitor on how popular a given Linux distribution is.
Most Linux distributions are free
Most of the popular Linux distributions these days have a LiveCD portion, including Ubuntu, PCLinuxOS, and even Gentoo. The most popular known specifically for LiveCD functionality is probably Knoppix.
There are many different websites that distribute a variety Linux operating systems. The most popular place for desktop distributions computers is Ubuntu.
gnome and kde
Nothing. Most Linux distributions are free of charge. There are some distributions that are commercially sold, though those sales are more likely subscriptions for support, not for the Linux distribution itself.
A Linux distribution, known as distro or flavor, is an operating system that uses the Linux Kernel. I think the most common one is Ubuntu.
Most Linux distributions will come with SSH preinstalled. If it's not, install the package "ssh".
Most Linux distributions are already secure. It would actually be more difficult to make them"unsafe."
Some will, if you install Mono. By default, most Linux distributions do not include support for them, though.
Most desktop Linux distributions (Ubuntu, Fedora, PCLinuxOS, OpenSUSE) are equally suitable for laptops.
bash (Bourne Again Shell) is the default shell in most Linux distributions. It was created as part of the GNU project.
GCC is already for the most part preinstalled in many, if not all, GNU/Linux distributions.