The version that the *buntus are built off- debian. Debian is normally lighter than any of the *buntus. I'd suggest 'stable' (6.0, 'squeeze') with the Xfce or LXde DE. KDE 4.X is too heavy, gnome 2.X is on the way out and heavier than Xfce/Lxde as well.

Your hardware is old enough that you (probably) wont have any closed souce video drivers, etc. to install......which is one of the main reasons why ubuntu is popular (lots of people seem unable to install the ATI/AMD or nVidia closed drivers with debian).

Debian still uses alsa, not pulse. Its more of a pain to try to get Rakarrack going with pulse.

What version of Ubuntu for 1 Gig system ?
 

Thank you all for your most informative replies. I've learned
a lot thank to you all.
I'm going to try Debian 6.0 Squeeze first because it
uses ALSA with out Pulse. Pulse really gets in the way
when you're trying to produce your own audio creations.
I'll try the Gnome 2x because I want to run the
Gnome Wave Cleaner program. It is great at cleaning up
.wav files. Gets rid of all kinds of audio problems.
If that doesn't work, I'll try Mint next.
I've got a copy of both Mint and Debian 6.0 some place
in the basement.
Really good of you all to give your time to answer my question.
Thank you very much !

Gnome programs should run in virtually any DE, not just gnome. Lxde and Xfce both use Gtk anyway.