Teh way I would knock one out would be too (note I'm not a small format or htpc person so no real idea on quality)
But I would get a small ITX/miniATX board with HDMI or dual HDMI out) seem quite cheap at the moment.
Stick a Pentium 'haswell' chip on it or AMD depending on which setup comes in cheapest and quietest.
A bit of RAM
An SSD
Stick it in a cardboard box an off you go.
oh and a little PSU preferably from a 'block'
The onboard IGP of the Intel should do as good a job as any, big TV's and our old ones will probably be no better.
That's the main box sone, then just whatever DVB T2/S2 you can find, if you have room for one inside I would do that.
If the quality is needed and you're really picky then I would run Sharkies codec if you are running under Windows or tweak whatever the Linux counterpart is to you taste.
I would Powerline the board as I have just moved over from my 'n' wi-Fi and reliability and speed is just superior where I live.
Stick a mechanical drive NAS somewhere and move the click click and fans away from the TV.
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That is at least where I would start looking, though there are some nice Atom cheap setups now.