Don't get too hung up on which distribution to install - it is the applications which really matter, and your main applications are the desktop and the word processor. I think you would be best off getting a distribution that has a wide choice of desktops and checking them out one by one; try XFCE, LXDE, Openbox etc. You can also try Gnome: you may prefer a richer desktop that is a bit slow to a faster but more basic one. Similarly you could try out the various word processors that are part of your chosen distribution.
(As an example, I am running OpenSuse 11.2 on an old Dell CPx laptop, 500MHz processor, 192MB of RAM. OpenSuse is not normally considered lightweight but during the install I just chose XFCE rather than KDE as the desktop. With Google chromium running with 5 tabs open, and a terminal with htop running, htop is reporting that I am using 99MB of memory.)
You may need to be careful how you install Linux: your computer will find it much easier to boot an installed distribution than a live CD. On this machine I installed from the network install CD without a problem, for Ubuntu based systems you would be better off choosing install
straight from the boot menu (assuming Ubuntu hasn't changed that much from what I remember).