I would personaly use Lubuntu. It is a very fast and lightweight OS. It also comes with some preinstalled apps so you ussually have everything you need.
Minimum supported requirements of Lubuntu:
266 MHz processor;
128 MB;
3 GB hard drive;
no fancy graphics
(I read someone installed on 128MB RAM and then removed 64MB RAM and it still worked,
not as fluid as previously, but still working)
About Lubuntu:
https://wiki.ubuntu.com/Lubuntu
Lubuntu WebPage:
http://lubuntu.net/
Other option could be Arch Linux and isntalling only the bare minimum and LXFCE desktop environment (this one is use by Lubuntu) - or if LXFCE doesnt meet you requirements you can try i3wm or openbox windows managers. Arch is the harder option.