How old is "very very" old? 386 have become difficult and not worth the trouble, unless it is some sort of research. 486s are OK as webservers, but the RAM requiremnets of the current stable version of Moodle is prohibitive. Pentium Classic (P5) is more reasonable.
I understand the question not as a general "best Linux distro" rather any Linux distro which will run a LAMP server on your hardware, right?
If it really is 'very very' old then I doubt you are. Moodle is actually quite resource hungry.
Most server OSs are reasonably lightweight in themselves. I use Ubuntu Server for what it's worth. You probably would want to start here: https://help.ubuntu.com/community/Installation/SystemRequirements#Ubuntu_Server_.28CLI.29_Installation
If that doesn't work then old faithful Debian might work better but you could be stuck without new enough PHP, MySQL etc.
I hope I don't sound too sarcastic, but how on earth are you planning on installing an OS (possibly on tricky hardware), setting it up and installing Moodle if you struggle even to download the OS in the first place?
You're right I should have explained about the computer's age. It has Windows 2000. That should give you an idea of it's age.
I just asked for help for help when downloading because I went to debian's page and saw many links for architetures I didn't knew. But I have a fair decent knowledge in computer science.