If you look at http://www.ubuntu.com/getubuntu/releasenotes/804
you will see the minimum system requirements for ubuntu 8.04 include 384 MB of system memory (RAM) for a LiveCD install and 256 MB for other methods such as the alternate CD.
On the other hand, http://www.ubuntu.com/products/whatisubuntu/xubuntu
shows near the end of the page that the lightweight version known as xubuntu requires 128 MB of RAM to run but 192 MB to install.
Hence, I suspect you need to upgrade your system before you try this. The good news is that the kind of RAM you need is so old and yet so common, you should be able to find some for free if you talk to people in your area. The machine is still viable as long as you do not expect it to be speedy. But it is unlikely to ever run fancy new graphics. Sorry to be so blunt, but I felt your expectations were a bit to high.
On the other hand, there do exist much lighter weight versions of Linux, like PuppyLinux ( http://www.puppylinux.com
), and some of them might be fine for your system as is though I have no good sense for which ones are any good. Perhaps someone else could comment on that.
Whatever you do, try to get more RAM in your machine as one of the most effective ways to speed up old machines.
I hope this helps!