You guys need to check the specs out on his machine.
He said 'old computer'.. For mythtv to realy work you need to have at least a 1.5ghz machine for basic functionality.
You can use a much slower machine if you want, but that is only for the frontend of the device... The server 'mythtv backend' would then take most of the load of transcoding tv content and ripping dvds and such, which requires very fast disks and a powerfull CPU..
(at least 120gig 7200rpm 8meg cache drive with a 2.0ghz AMD cpu for a pleasent experiance)
So Linux-based Mythtv wouldn't work out to well if all he has to work with is a old like 400mhz machine or so.
And he already said that he would use GeekBox, which is a linux based distro specificly designed for multimedia stuff.
See:
http://geexbox.org/en/requirements.html
This thing won't give you the TiVO like functionality but it will work with older machines just fine provided you have a halfway decent video card and enough ram.
So he was already going to use Linux.

But he wants windows, too.. so the obvious answer between WinME and Win98 SE is Win98 SE, although Win2k may work out better in a pinch... it's much more stable and has more intellegent memory handling capabilities.