I had one of those low-powered mini PCs briefly. I found them too slow at running Windows and an overall PITA. For the tasks listed by the OP you don't need to be running Windows at all IMHO.
I only mention it, as you sometimes have more flexibility, than some of the other platforms.. can do ADDITIONAL stuff on it per say that the others may not, etc.
As for the mini PCs.. depends on what specs you get. And what you install on it. THe one I have ran, was running a win7 light install, and FLEW.
Likely at this point if I re did one, would put a win8 light install on it, with a SSD drive.
I guess a lot depends on what/how you are running your stuff as well.
If that PC is doing all the decoding, etc, than it will need to be more powerful.. vs running a media server setup where the server does most of the work, the playback device doesn't need to be quite as powerful.
Just giving the user some options
I myself, run multiple things in my house.
Minipc playback on basement setup, TV does the playback via built in apps in living room, and airplay through an apple TV in the bedroom.