I think you need to clarify what you want to do.
Do you want to backup the existing startup drives of each machine, or just select data to clear space?
In honesty potentially worth doing both.
Do you want a bootable external drive/drives with a copy of the existing installation/s?
Do you simply want to store an image of teh startup drives which could be reinstalled to the internal or external drive for startup purposes?
For simple backups you could certainly use Time Machine, preferably using separate drives/partitions for each Mac. You'd be best starting from a new empty/newly partitioned drive, though you can also store data alongside Time Machine data.
As much as Time Machine is theoretically simple to use, I personally prefer to manually backup either to bootable clones or large disk images (you could store several on an external) which could be restored to a bootable drive if needed. You might want to look at Carbon Copy Cloner or SuperDuper demos to see if they'd suit you.
Remember that if your wife clears space on one Mac, then any 'backup' is not really that as the data will have been moved to an external and unless you have other copies is vulnerable in case of the external failing. Many would advocate keeping several backups, and a backup offsite in case of fire/theft.
Ultimately it all boils down to what data is truly important and needs to be backed up and available for posterity - certain emails, documents, family photos/video would be the most important for most. Media like iTunes video, CD rips etc may be 'valuable' but for the most part could be replaced (or redownloaded from the cloud in teh case of most iTunes purchases - though not guaranteed forever).
In essence I think you need to clarify what exactly you are trying to achieve.
Forget software RAID with external drives. It will more than likely bite you.