Design For Automatic Remote Back System Wanted.

I'm starting to think about what I need to do a 'Nightly' back up on my daughters laptop (Acer With PCLinuxOS on it ) when she goes to uni next year.

I have contacted the two main uni's she is interested out of her five offers and it looks like the backup will have to be instigated from her laptop end, because with them using Nat For there IP address's as I will not be able to reach it from my end.

I will be using 'LuckyBackup' luckyBackup - backup and sync utility as it has a good ssh remote backup part.

I have a speedtouch 636 None NATing router with a block of my own fixed IP address's (with it's firewall turned off).

From the speedtouch it goes into my Dedicated Firewall 'Smoothwall' Express Open Source Firewall Project (The Free one ) I will put a DMZ.

From DMZ it will go to a 'to be built 'Backup server' (lightweight Linux based) .

I need any advice about making the connection from her laptop to my backup server and what I will have to do about making my server hidden but accessible from the internet.
Any tips about what to look out fo and do to make it a safe system and not Hackable !.