I am looking for a light weight Linux for a PC that runs at 200 Mhz with 256 Megs of RAM. I was thinking maybe Lubuntu, as the system requirements state it needs at least a Pentium 2 generation with 128 Megs of RAM. The GUI is not all that important to have, so would I be better off going with something like Ubuntu server? I was kinda hoping to go with a Ubuntu flavor due to their great support base, but I am willing to try other flavors.
I think you'll do fine with just about any distribution (save for Gentoo or LFS maybe) if you install a light desktop environment such as FVWM, fluxbox, openbox and so on. If you care for Ubuntu you can always select a server installation and install a desktop environment from the command line afterwards, there's no need to have a specific Ubuntu deviant for it.
You should try Tinycore. It just needs 10MB with GUI. But if GUI is not a requirement, then you can pick any distro and not install the desktop environment. That should save you boat loads of memory space. I did the same thing with one of my old laptops. After few days, I installed X to use firefox.
Try Slitaz. It's small and good looking.
If you want a good overview of Linux distributions that will run on older or lower spec hardware, it would be worth your time browsing through the posts on KMandla's blog.
He has documented the performance of a large range of distros on these sorts of machines, with insights about the strengths and weaknesses of each. He also has a wiki which features lighter weight CLI applications that run well in these environments.