I have a full-height server rack with large, loud, noisy, power-inefficient servers, so I can't provide much of a good suggestion there. I did want to say that you might want to seriously reconsider using a single 10Tb hard drive.

Hard drives fail, and with a single drive, in the event of a failure, your data is gone. Using several smaller drives in an array provides redundancy, so that in the event of a drive failure, parity information exists on the other drives. As long as you replace the failed drive before anything else fails, you don't lose any data. There are multiple different ways to do this, but I'll use RAID as an example. In RAID5, one drive stores parity information. If any one drive fails, the array will continue running (albeit slower); you just need to replace the failed drive and allow your controller to rebuild the array. In a RAID5 configuration, you lose the space of one drive to parity. So if you have 4 4TB drives in a RAID5 configuration, you would have a total of 12TB of usable space. RAID6 lets you lose two drives, but you also lose two drives worth of space to parity, meaning your array would be more fault-tolerant, but you'd only have 8TB of space.

There are many different RAID configurations; far too many for me to go into them all here. You also have something called ZFS, which is a file system with many similarities to RAID (and a LOT of extra features... like snapshots). As an example, I have 12 10TB hard drives in my NAS. Two groups of 6 drives are configued as RAIDZ2 (similar to RAID6), for a total of 40TB usable space in each array. Those two arrays are then striped (like RAID0, so that data is written across both arrays with no redundancy at the striped level). In total, that means I have 80TB of usable space, and in a worst-case scenario, I could have 4 drives (two on each array) fail without losing data.

I'm not suggesting you need a setup like mine, but you could probably fit 3 4TB drives in a small case, use RAID5 or ZFS-RAIDZ1, and still have some redundancy. To be clear, RAID is not a substitution for a backup, but it can go a long way toward ensuring you don't need to use your backup.