About two years ago I decided to start researching Linux/Unix myself, it's been quite a learning process but I've found a lot of information online that will help to get you started.
The first real question is 'what is it you want to do'? Once you answer that you'll know which programs will be good to start with.
Ubuntu is a very popular system that is easy to install and use, and still very robust. There are Desktop and Server versions depending on what you want to do (
http://www.ubuntu.com/GetUbuntu/download). Both come with a full suite of applications, like Open Office (like Microsoft Office), media players, Web browsers and everything else you would expect.
Like most Unix operating systems Ubuntu also has a application download feature that will allow you to install other applications you might want right from the Internet and install the automatically.
If you are looking at doing more serious serving, for a Web site or database serving, you might want to look at Debian (
http://www.debian.org/distrib/). Debian has support for higher end processors and hard drives and supports more enterprise class services. It also has all the same features as Ubuntu Server, but more native administrative abilities.
Finally, if you just want to fool around a bit first and get used to the Unix world then Knoppix is a great Operating System that will run from a CD (
http://www.knoppix.org/). You can simply insert the bootable cd in any machine and it will load a completely functioning operating system independant of what is on your hard drive. It has Open Office and the other applications and is a good training ground for Unix. You can also install it permanently on any machine if you wish.
Good luck!