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UBUNTU - The most popular Debian off-shoot , good for beginners. (Update February 11,2009)
If you have never used Linux go for Ubuntu.

It is one of the easiest to run. And it has everything.

Ubuntu is based on Debian Linux. You can run and try the Live CD before installation though the Live-CD shall be slow to run. You can install Ubuntu as a standalone OS or alongwith your other OS as Windows, you can select your OS when you boot.

It has graphical package manager synaptic to add or remove programs, there is a simpler add/remove program too. When you add, packages get downloaded via net and get automatically installed.
Ubuntu is FREE and Ubuntu has excellent Forum Support.

here is excellent support at ubuntuforums.org, busy round the clock, 24/7/365, no holidays.

As far as applications are concerned, there are more than 10000 packages in the repositories to choose from. All FREE.


32 bit or 64 bit ?

If you have 32 bit machine, you go for 32 bit only. In case of 64 bit machines, you can run either, Most packages are available in 64 bit and there are ways to run 32 bit software in 64 bit OS. There is a separate forum for 64-bit at ubuntu forums.