regarding to desktopenvironments like Gnome (Ubuntu) or KDE (Kubuntu) or XFCE (Xubuntu) I'd recommend to take a look at the graphics-hardware of the old computer. At least KDE (the recent releases) needs a relatively recent graphicsadapter. XFCE doesn't use that much resources, so it may be that Xubuntu is the better choice for you.
You may post the output of
so we can check which graphics-adapter you have.
Note that most likely the system can also be installed in the 64bit version.