I'm asking this question on r/AndroidTV because I really like Android TV and would prefer to stay in that ecosystem (I was thinking an Nvidia Shield might be best), but I'm open to another solution if that makes more sense.

I have a collection of movies I've purchased through Google Play, Amazon, and Vudu (I use Movies Anywhere to get them all in one place). It's great for streaming, but I'm moving to a country with slow Internet speeds that likely can't support streaming 4K movies. I know that these services allow you to download movies for offline viewing, but it looks like that only works on phone apps (and maybe Chromebooks?), and I want to watch these movies on my TV. What's the best (legal) way to download these and then play them on my TV?

Like I mentioned, I'd prefer to buy an Nvidia Shield and use that, but again, it looks like the app on the Shield doesn't support downloading the movies for offline use. Is there a way to make that work?
Or should I just buy a cheap tablet or Chromebook, download the movies to that, and then use an HDMI cord to the TV? I think you can download to an SD card, but I'm not sure what size SD card I'd need for the 40 or so movies I have. Can you also download to an external hard drive (I already have a couple of 1 TB external hard drives laying around, so that would be easier than purchasing a large SD card)? Could I bypass the HDMI cord and stream from my device to the TV (assuming I had some sort of Chromecast device on the TV), or would the slow Internet speeds preclude that (I'm not sure if there would be a difference in speed streaming something within my home WiFi network as opposed to streaming from a website outside my home WiFi network)?

Apologies if this isn't the correct subreddit, but I figure you guys would have encountered this type of problem before. Thanks in advance for any guidance you're able to provide.