Lots of Chinese sites sell these cheap Android boxes, but I've read lots of bad reviews about them on Amazon, reliability seems to be a big problem with them, which brand do you think is the most reliable: Minix, Tanix, Vorke, Xiaomi, Beelink, Meecool, MXQ, etc.?
Android boxes are garbage, so I'm not going to recommend any of them. I will however recommend a cheap Android TV device since you're in the Android TV subreddit. A Mi Box is the defacto affordable Android TV device. Other than that, you have to look at the NVIDIA Shield TV which is $180+.
As said by one of the previous posters, I'd recommend going for one of the Google-sanctioned Android TV boxes, the Xiaomi Mi Box being your most cost-effective and reliable option. If you however want the more premium experience, you might want to consider the Nvidia Shield TV though it will likely be overkill for your needs by the sounds of it.
As for your "confusion" regarding Android boxes vs Android TV boxes, it's a common oversight for those who are less informed but not the fatal blunder that some on here are accusing you of. Apparently you've offended the sensibilities of several overzealous purists when it comes to distinguishing between the two. They need to take it down a few notches. It's so unnecessary it's almost silly.
I don't know why I got so many downvotes, I just asked a question, I don't know how these things are called or what OS they have, I'm simply interested in a cheap, reliable box that can be attached to the TV and play movies...
You are in the WRONG Sub-Reddit.
This is for Android devices running the Android TV OS not Android boxes you connect to a TV that run the tablet/touchscreen Android OS.
Those Android TV devices mainly being NVIDIA Shield, Xiaomi Mi Box, Channel Master Stream+ various TV running Android TV & a few I've forgotten.
Having said that some of the MECOOL devices run the (Nougat) Android TV OS. But have no Chromecasting capabilities. The S912 Pro L is the fastest.