Ok so buying a new PC is a good idea, especially the age and more so the OS, WindowsME was a nightmare. Although some rumours on the interweb suggest Vista may be similar. Although that as I said may just be rumours.
If you're looking at gaming with your new PC then shared graphics isn't the way to go.
I'd recommend nVidia over ATi, however there isn't much difference when you compare like for like to be honest.