Depending on the board in your mini-server, you may have enough SATA ports to plug in directly. I have a system similar to what you’re describing (N100 with 4x 2TB HDDs with 1.5TB data): 2 of those drives are set up in RAID1 (mirror), and once a month, I plug in one of the spares, rsync the array to it, and unplug it. Every 3 months or so, I swap the offline drive with an offsite drive. I used to use a USB dock for the offline drive, but I got a 3-bay hot-swap enclosure to make the whole process faster and easier.

The server shares the array via NFS and SMB, and it is absolutely a NAS for all my other systems.

If you expect to exceed 2TB data within 2 years, then you’ll need to replace all 4 of those 2TB drives in 2 years. You might, today, get a pair of 4 TB drives and one 2TB, use the 4TB as your main storage, the 2TBs as rotating backups, and wait until you actually outgrow 2TB to upgrade the backups.