I put a rack/cabinet in the laundry room, with a QNAP NAS in there, Plex server is running on the QNAP, then an Apple TV 4K connects to that and feeds the TV.
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 have a similar setup myself. I use basically an older PC running Proxmox + openmediavault as my NAS (and a bunch of other things, including Plex). I currently have an NVidia Shield and 'Chromecast with Google TV' as clients, as well as a couple phones and tablets. It is pretty hands-off and my family can all use it just fine.
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.
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.