It turned out that the things we needed were all available at Orbit. I chose the Asrock K7S41GX, a highly integrated motherboard: LAN, sound, VGA all on-board -- for 50 euros. OK, so it's not top-of-the-bill, but it works. And if all you're doing is internet and video-conferencing, you don't need lots of fancy hardware.
For memory, we used the PC2100 256 MB module that xaviar_nl had in surplus, that I still had lying around (because I had forgotten to return it when I found out that I had no use for it). We added a Sempron 2300, a second-hand floppy-drive and a cheap DVD-ROM, and that was that. When we stepped out of the shop, klik reminded me of the fact that we'd also need a keyboard and mouse to go with the system, so one minute after having left, we were back again! We chose a Logitech optical wireless desktop-set, an older model that was discounted. Now the keyboard and mouse can easily be stowed away when the system is not in use.
The system is now up and running. It runs smooth, but because there's little memory (and the VGA adapter also uses a chunk of that), there's a lot of swapping when running more than one process. Perhaps we need to invest in another 256 MB module, they're not that expensive...
I also ordered ADSL from Demon, and I will need to mail the people from Routershop.nl about the hardware I will need to tie it all together wirelessly. The desktop case can only hold low-profile PCI-cards, so perhaps we'll need to get an USB-solution for that machine. Not ideal, but the desktop-case is too good a fit to compromise on that front.
I'm also given free reign by my dad, which is pretty cool. I get to do it my way.