I don't mean to insult you or your laptop at all, but speaking purely from a necessity standpoint, that laptop is REALLY underpowered, even for a server. Even the smallest distro I can think of, Puppy Linux, is going to eat up around 300 MB of your RAM. Then, considering you never have an even GB of RAM, it will always be less, you would probably only have about 600 MB of RAM to use. That's ALL BAD for a server, considering that servers have to do a whole lot at once. And RAM is what does most of the heavy lifting in this area, not the processor.
However, I think that it is still worth the test drive; just to see how it handles. What's the risk in trying a Linux distro FOR FREE? So, here are a few Linux distros I would recommend:
(Excellent library of apps. Excellent support. Best option in my opinion.)
(Based on Red Hat, so support won't be awful. Neither will be your library of apps. Not as good as Puppy in my opinion.)
3) Vector Linux
(Based on Slackware. I never used Vector or Slack, but this appears to have the lightweight requirements of Slackware that's a bit more user friendly. ((Other wise known as not as big of a pain in the neck to work with.)) I have no idea how good the packages or support are, but it can't be too bad since it's basically a streamlined version of Slack.)
Please let me know if this helps. I'd be glad to do what I can.