Backups using Mac Mini Server & Time Machine
I'm not sure what you're exactly asking… but let's try.

If you have a Mac Mini Server and want to backup 3-6 machine's data, I'm assuming those machines save that data in the Mini's storage. (If not they should).

Then You can use a combination (or all) of the following:

1) The "Data" is stored on a mirrored drive (RAID-1 or more). For redundancy in case of hardware failure. Doesn't count as backup but counts as immediate hardware failure protection measure. Keep working even if the drive fails. 

2) The "Data" Drive is part of a Time Machine to an external drive(s) (those drives can also be mirrored for an extra layer of protection). If your time machine drive fails, you have the mirror to keep working until you're able to restore the offending hardware.

3) A final, good idea, is to clone the drive (internal) into yet another external drive to have a copy-cat of the data in case everything goes to hell (You can use tools like SuperDuper or CarbonCopyCloner for that.

4) If what you want is the minimum amount of downtime in case of hardware failure or total software failure, you might want to have backups of at least one of each of your Macs so you can boot from an external identical drive if one machine fails (while you reinstall the original). Assuming the data is never locally stored, of course. Otherwise, you'll need a TimeCapsule with a huge external storage to let each Mac backup over the air (or net) to the Time Capsule as well.

Think of backups and redundancy as layers. The more you have, the more protected you are against external factors. 

All this would be useless if you don't take your backups offsite…