LM386 is a decent amp.
Many TVs made in the last 15 yrs or so have an audio-out. It's not a good driver for headphones in itself. Any stereo can plug into that and has a quality headphone-out though. Any number of cheap, smaller products could also be adapted.
Building an amp is not a big deal, but still a lot to learn, a lot of parts hunting, and may end up being housed in a huge box. For something that only costs $10 or so to just buy I don't see a reason to make one. I mean you can buy an old stereo at a garage sale for one.
The big question is how practical is it to run a long cable across the room , up the couch or bed or wherever, and not keep tripping over it. Well, there are radio and infrared headphones. In fact radio transmitters that plug into your iPod or CD player so your car stereo can tune into it without a cable are common- real common. That can plug into the audio-out from a TV and you can use any sort of radio-headphone to listen to it from across the room without a cable.