That looks like a good little machine. Nice HD, good RAM, the processor is a tad old, but Linux doesn't need a powerhouse anyway.
For Linux, you will most likely want a distribution that's easy to set up and run. Like you said, you want internet connection and basic functions(word processing, image editing, media players). Most distro's include plenty of pakages to make Linux as functional as Windows.
I would suggest
Mandrake,
Red Hat,
SuSE, or even
MEPIS(I've heard good things).
I personaly only have experience with SuSE, but I plan on switching to MEPIS soon.
You can get any distro for free if you download them. If you want the discs shipped to you, you have to pay a little bit of money.
There are also Live CD's that you can pop into your CD drive, boot from the disc, and play around in Linux without installing it. Knoppix does this, and MEPIS is an installable Live distro.
If you decide to download the distribution you choose, you'll need a CD burner, a MD5 checksum program to make sure you got the file completely, and a program that will burn ISO files. Nero can do this, and does it well.
Once you have the discs, pop the first one into the CD drive(some distro's have multiple CD's), reboot the machine(if it's already booted and running), and a diologue should come up with instructions on installation. Once it's done installing, it should reboot, let you set up user preferences, and you should have a running Linux system with a GUI.