I would seriously just clone the whole thing from the beginning.
There are secondary issues to consider with incremental backups, such as fragmentation of data on the backup drive. You'll be best to quick format the old drive, or just delete everything and empty the trash, and copy a new and fresh sequential backup to the drive.
Yes, it will take a while -- so do it overnight.
My last big backup was a 2TB drive clone, and that only took maybe 10 hours -- all of which happened while I was asleep. I often think Mac OS X USB2 copy works faster than Windows XP USB2 copying, so it could be even less time.
Using "backup software" adds a level of complexity that can simply be avoided.
I'm also assuming you're simply backing up data here, too -- your work files from their own drive. This isn't a backup of the operating system, the installed software, etc. If you need to backup the computer's operational files, you can use Time Machine. I prefer
Paragon Drive Copy for Mac OS X. But again -- only for the system, not for work files backups. For work files, simply drag and drop to do basic copying between drives.