I run Debian Sarge. Do a net install and then only install the programs you want. Another thing that will help your old machine is to recompile your kernel. But as a Newbie, you won't want to take that on right away. If you go with Debian, google for the "Very Verbose Debian" and also google for "Compiling kernel the debian way".
Now, in the event that you want to see some other options, take the two quizzes in my signature. They'll help you pick a distro for you. But Debian is the way I went on my Celeron 400MHz when I was brand
and I've never looked back.