If it's only got to *serve* media, go as low spec & noise as possible...
The 1800XP with even 256 ram would probably be more than ample!
Also, if possible use 2000/2003 server (I know you can also tweak XP into doing it, but I'm lazy

), and RAID-5 the disks together (nothing is more annoying than trying to recreate 200Gb of media from backups when a drive dies).
Depending on the layout of the apartment (ie if you've got a cupboard or under-the-stairs closet you can stash the machine in), look at getting a Hauppauge MVP or similar thin client. We have one in each room and it's a really neat way of watching media files on the TV without all the faff of having a PC