Take a look into duplicity, rsnapshot and rdiff-backup if your primarily backing up linux machines. If you want to backup windows clients as well take a look at jbackpack it's pretty great: http://www.nongnu.org/jbackpack/
How are you moving the files? You can do Rsync as others have mentioned, filesystem snapshots/dumps, timemachine, windows backup, etc...
Having a samba mount may or may not simplify things depending on how which method.
Ok, are your mail and billing servers also linux? If so then you can just do/make a script to do
scp fileToBackup.file account@backupserver:/filesystem/location/for/backups
and voila, backups are done.
It should work fine, but don't expect great speed out of it, you're really going to be limited by IDE ports (or sata1 ports) and associated hard drives. A decent e-350 board might be worth investing in just for the sata3 ports (and thus faster disks).