I think you're confusing a few ideas here, and it's hard to understand what your main goal is. Let me see if I can break down what you want here:
Small form factor if possible
Storage expansion
Low power (antithesis to 3.5" HDDs)
NAS features? (unclear here)
If you're just trying to run containers easily, Synology NAS that support it (certain tier) are really easy to use, and you won't have to worry about hardware except inserting the initial drives to use.
If you're worried about cost, sure, building your own is going to be the best bet. If you're not expecting to really tax the I/O of the drives, USB 3+ won't be the worst thing in the world, but the management of a storage array over USB will be problematic if doing it yourself.
Lastly, it may help us if you describe what you're actually trying to to host on this hardware. It's the difference between someone suggesting a very low power CPU like an N100, or a lowER power CPU like and AMD that has a bit more upfront cost.
If any of this is confusing, just have a look at Synology or Qnap maybe. It'll be easier to manage in the long run if you're not comfortable or enjoy fiddling with hardware.