I've been using Chromecast happily for a few years. I'm looking for a local device for a couple reasons (more reliable/less buggy and local USB playback).
In particular, I need:
Mi Box 3?
Best device period is the Shield TV. The only other option that runs the Android TV operating system is the Mi Box.
a Mi Box if you are going cheap and an Nvidia Shield if you are looking for the current best
Shield TV is the best hardware out there IMO, is you can afford $200 then that is what you should get.
The best for performance is going to be the NVIDIA Shield TV, but that will be overkill for your requirements.
I think the best price/performance thing right now is the Mecool M8S Pro W. It's like $40 right now and has actual Android TV Leanback interface.
Xiaomi Mi Box will do that, but you need a powered USB hub in order to use external drives like the passport. Either Kodi or VLC will let you playback whatever you have on the drive (Kodi will work better tho). Avoid Plex as that has the annoying habbit of taking your carefully organized media and clumping it into one big directory.
Walmart sells the MiBox for $59
I own a MiBox, have it in my bedroom. Its about 30' away from the router, through a wall and I dont have any issues streaming channels from my HDHomerun Prime (the MPEG2 bitrates are huge)
Wait for Google I/O or buy a used Nvidia Shield.