Just use Debian without a GUI. I have a box in the corner of my apartment that has a power chord and a LAN cable going into it -- I just SSH to it or use NFS to access shared partitions. Truth be truthed, though, 256MB of RAM is going to be a tight fit for a Debian LAMP stack. With similar services to what you propose, my machine currently idles with twice as much memory used.
total used free shared buffers cached
Mem: 3025 2977 48 0 261 2147
-/+ buffers/cache: 568 2456
Swap: 8283 0 8283