You could try NAS storage. This will connect to your router rather than directly to your machine, but they tend to be more robust, and allow sharing more easily.
What they also can have is several bays. This means you can add extra storage (drives) later, or you can use multiple drives for disk redundancy so that it can keep going even if a drive fails. Multiple drive NAS can also read/write faster in most circumstances.
I have used QNAP for years with no problems - http://www.qnap.com
- and I think most of their current stuff supports 3TB drives (which you can multiply with more drives to give higher total storage). If I need to increase capacity I can just replace the drives with I have larger ones one-by-one and the NAS will rebuild itself with higher capacity.
A neat solution which might make things easier in the long run, although there's a little more tech to it than plugging in a USB HDD or similar.
Hope this helps as a starting point.