No halm in trying mandrake, Just try to make it a very minimalistic install.. If you don't succseed you can always try another distro.
I think im with Aykon that slackware may be your best bet. But the real trick really is making certain you don't install to much, and not having more services running then needs be... I personly bleave SSH would be a great service to have running since you could use your current windows box for interfacing with the machine by putty(google it, easy to find) it might be more convenient then having to change machines all the time, Plus you can use your current web browser etc to search for stuff on running and configuring linux insted of installing one (dunno how well moden webbrowsers work on that processing power)..
So go minimal, and if you don't succseed, try another distro..
Definatly don't install Gnome or KDE, desktop enviroments.. Fluxbox, Blackbox, twm (exceedingly old :D), sawmill or window maker should all be great choices for window manages, ( I would suggest window maker... I have a soft spot, Its a clone on NextSTEP/OpenSTEP that mac os x is based on ).
Try installing firefox if you have enough room, It might run ok..