I naively put an old LaCie 1U server under a Lack table 13 years ago, thinking it would be a great media server in my living room. I had no idea how loud rackmount fans were. It was obviously unusable for watching any kind of media.
What drives me nuts is power supply noise actually. I finally bit the bullet and got a Mac mini for my home office.
For those playing at home, buying a 2U or even 4U rack will on average be quieter (still sounds like a jet engine just after reboot until the SMC comes online).
Supermicro builds some workstations[0] which were quite quiet back in Xeon 5xxx days.
[0] https://www.supermicro.com/en/products/x11/systems/workstati... be sure to check for the 'quiet fans', not the 'heavy duty' ones!
A commercial box, like NVidia shield, Chromecast, Roku, Amazon Fire stick or AppleTV. This is by far the easiest as you get a remote, a "10 foot user interface" and they work with online services like Youtube, Netflix, etc. If you care about everything being open source software this obviously isn't a good option.
You can also DIY your own box on a Raspberry Pi. Be prepared to do lots of tinkering, though.
The other option is to get the media server's UI remotely. Long HDMI cable, HDMI-over-cat5 or wireless HDMI gets audio/video; some of those also do USB, or you can do wireless control if it's close enough. Almost as much tinkering as a Raspberry Pi, but could be cheaper if it's not far.
Another big benefit of the first two options is it scales to multiple clients, if you have more than one TV.
Even more than that, I'll bet a lot of people who are connecting a media PC to their living room TV also have another PC somewhere in the house. With a long HDMI cable, you can connect an existing PC to the TV, thus saving the entire expense of a new PC. This is particularly interesting for gaming, since a good gaming PC is a lot more expensive than even some of the longest HDMI cables.
I like this better than trying to do some sort of long HDMI cable setup, because the HDMI ports on most NAS units out there get old rapidly, don't support HDR and high bitrates reliably, etc. This way, it doesn't matter if the server is brand-new and fast enough and all updated for the latest video standards. As long as it can push the data out fast enough via Ethernet, you're good. Updating an Apple TV every 3-5 years is a lot cheaper and easier than getting a new server every time. And a good NAS is a lot cheaper than a full-out server would be.
I'm content to replace the relatively cheap client boxes every few years. That said, I think I've had the Shield for over 5 years now and other than the original remote being bent in half (likely a jumping-on-the-couch-related failure) it's still going strong.