openbsd?
actually I used to use trustix for all my servers I think it was around 300mb for a full install.
For a setup dedicated to running a single program like that, how about setting up a pxe boot environment that uses something like dsl or puppylinux as the boot image and is tuned for only running that single task? That way you don't need any drives at all in the computers, just cpu ram and a network card. Less power wasted that way spinning an otherwise useless drive.
I pretty much have went the low power route at home now so I haven't used an actual x86 based server for a year or two so my knowledge of current distros might be out of date.