Don't try TM with a NAS with that much storage, they are not approved by Apple.
Best means different things to different people.
Wireless will be agonizing slow, so attach a drive larger than 4TB to the mini.
USB3 drives will work (WD elements is less than $100 now days). Thunderbolt will work better.
If you want the initial backup to take less than a day and be more responsive, then buy a OWC Thunderbay last years model (TB1) from their clearance page. Load it with two 3TB NAS type drives or three/four 2TB NAS type drives. Use disk utility to RAID0 them. This will give you 6TB (or 8) of decent speed storage. But if you meant the least amount of money to get by when you say best, then this is not the approach you want. This approach will provide the much better performance and reliability, however. A bit better is to populate the enclosure with four 3TB drives Use disk utility to make two RAID0 pairs and then either tell time machine to alternate backups between the pairs or mirror them with disk utility. I perfer letting TM alternate.
If you insist on backing up wirelessly (or over ethernet), buy a airport extreme (if you don't already have one) and attach a USB drive larger than 4TB to it.
