Don't use NTFS as it will not support hard links. Symlinks may also be an issue, not sure.
Best method of doing the copy will probably be rsync, since it will only copy the delta (changes) instead of having to recopy everything. There are also utilities (some based on rsync) that will save individual deltas so that you can restore to a specific backup.
However, if you have the luxury of being able to shut down Zimbra and only needing to restore the entire server to a periodic snapshot, then lvm and/or virtualization would be worth your while to investigate. In fact I've seen suggestions on the forums that there are ways of using lvm and virtualization that don't even require shutting down the services, but I haven't personally had time to investigate. See
Zimbra OSE backup without stopping the services and
Hot Backup Community Edition w/ DRBD.
EDIT: Also worth considering, VMWare Fault Tolerance, as mentioned
here. But it's not free.