Hi.
The questions that theNbomr posed are all good. The requirement that the solution runs across a network helps narrow the field of choices. However, you could have a blended solution -- backup locally, then transmit the backup across the network. The last time I searched the Debian repository for
backup, I got almost 100 hits.
I usually advise people to look at
http://en.wikipedia.org/wiki/Backup for background, then look at their vendor forums, although most of the solutions are common across distributions.
I'll be interested in what you finally chose ... cheers, makyo