For you I would recommend Damn Small for 3 reasons.

1. DSL is designed for that kind of hardware you are sporting.
2. You are a Linux first timer and going to Slackware as your first distro may be frustrating for you. Slackware is not exactly known for being easy. (although it is once you KNOW linux).
3. It is Debian based which makes installing new programs easier for you because you will have "apt-get" and Debian's huge repositories.

As a Bonus you can run DSL as a Live session to test it out to see if you like it. Once you install it to the hard drive it basically becomes Debian.