You have two main options -- one is a cheap external 3Tb or so drive over USB3, which will be ok for occasional storage or backup. I have one of these as a secondary backup device.
But for more speed and reliability, I wanted a "primary" external drive and eventually settled on the LaCie 2-big Thunberbolt 2. There are options from 6Tb to 12Tb I believe. I chose the 8Tb (which when arranged for security has 4Tb of available space). It's exactly what I wanted, small and tidy, fast and (so far) reliable.
Surprisingly, it was significantly cheaper to order it from the Apple store here than to buy it online at one of the many computer retailers.