I couldn't find anything official but my experience:
64Bit, I know of no other requirements.
My idle docker machine is consuming ~400MB, most of which is the Journal. I had trouble starting when I set the initial memory balloon to 256MB, I would recommend at least 512 (And then configure a swap disk, I think they changed filesystems but btrfs
doesn't support swapfiles).
Docker is pretty thin. I doubt you would notice a per container overhead. So just look at what you are running in the container.
Also don't forget to consider the disk cache, If you are tight on ram then disk IO will suffer.
Tl;dr: If it is 64-bit and can run virtual machines, it will run containers MUCH better.
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Thomas