I'd encourage you to try out Puppy Linux:
http://www.puppylinux.org/
It's a version of Linux, like Ubuntu, but specially developed for those who want very fast speed, often with older computers.
It'll run like a dream on your machine. It also comes with a ton of software built-in, including a web browser, office package, etc.
It's easy to download and burn a live CD with it on, and then you can boot from the CD and try it out, without any change to your internet drive with Windows on. If you don't like it, just restart and take out the CD, and Windows will be none the wiser!
It's backed by a good community who work at keeing it up to date and secure (unlike Windows ME), and can even be set to run entirely in RAM, making it run faster than even many of the very latest PCs.