Re: Recommendations for NAS-based home media set-up
I have a similar setup in my house. Synology NAS. It's a few years old but can stream HD video to a single device no problem. The new ones are obviously better, they're really easy to set up and the OS is great. You can configure the security and prevent access from outside. Also, you'd be able to stream multiple videos at once, but may hit problems if streaming multiple HD films (router limitations, spec of the NAS if it's a lower end one, WiFi signal etc.)
You didn't mention if you had any games consoles, but if you have a PS3 connected to one of the TV's this can pick up the content on a Synology NAS no problem, although it (disappointingly) won't play mkv vids. I'd assume a PS4 will do the same thing.
In addition, I have my main PC upstairs in the office (connected through WiFi), and an old HP SFF PC hooked up to the TV in the front room, wired to the router. Intel Core2 Duo, 4GB RAM, low end graphics card with HDMI out, Win7 running XBMC on startup. Not the best spec but works perfectly well as a media player/ occasional browser. You can get some really smart looking, low power, compact media PC barebones setups if you're willing to fork out. It all depends on your budget really. A PC has the added benefit of being able to store files for playback if other devices are eating up bandwidth.
As others have mentioned, there are some cheapo Linux plugin devices that can play a host of media files, as well as RPi. These would be a bit less power hungry than a PC. Also, some smart TV's will pickup NAS content.