My father wants a device to attach to his desktop monitor where he can browse the internet. He's got a PC but is tired of the less-than-snappy performance, and long boot times. I thought of buying a Xiaomi Box S for him, but I'm concerned about the CPU/GPU specs... Do you think he'll get a good browsing experience? We already have a good bluetooth mouse / keyboard combo, and will connect an ethernet hub to it.
In his own words: "I want the browser to be as fast as it is on my phone"
The MiBox S isn't really the best idea for this. It's designed pretty much exclusively for viewing media on a TV. It doesn't even come with a built in web browser.
If you're just looking for something in that price range that he could use to browse the web, grab a Raspberry Pi, a case, and an SD card, and set him up with a basic Raspbian install. You mentioned he already has a PC, though, and if it's of anything resembling a recent vintage, I doubt a Pi, or anything else in that price range, will outdo it. A better idea might be to try to figure out why his browsing is slow on his PC.
If his PC doesn't already have an SSD, I'd invest in one of those and set it up as his boot/application drive before I'd do anything like trying to replace his PC with a low-power Android/Linux box.