Ok cool, well those specs will contain a Slackware installation-- though I am NOT SURE
about a P1 CPU
; you would need to check on that (slackware.com). If you decide to try this out, I am not sure whether to suggest Slackware 11 or Slackware 12.x but I run 11. The reason for being unsure is that with an OLD computer, a super-new distro *might* have troubles with some of your older hardware. This is just speculation, but someone else may be able to provide more insight or opinions.
When you do the install (of whatever distro) many will by default boot up into a NON-Graphical runlevel; meaning that you will start off at the black DOS-like screen with a login prompt.
The general idea here is logging in as root, then type "startx" or "telinit 4" which should start up the graphical X server (which provides a graphical login for users after they have accounts).
NOTE - Some distros use "telinit 5" or "telinit 3" but most common is 4. Slackware will start the X server with "telinit 4".
Now, you should be at the desktop, where you can make a user account, or whatever suits you to do next.
For a desktop environment, Slackware offers a selection. You may not want to pick KDE, as it is the biggest, most full featured; it is good, but very heavy-weight on your slow machine. Up to you, but I would select XFCE when I got to that part of the install.
Best of luck, whatever you try