x86 is impossible unless you know for certain the app(s) you want to use is compatible with the hardware you choose.

I'm guessing you don't plan to stream from anything other than your own library? No commercial streaming apps will work with non-certified android hardware due to DRM. And the hardware software combo must be certified on a per app basis, so that means you have to buy an off the shelf device and cannot replace the OS if you plan to pay for streaming services.

You are also unlikely to find any pre-built images for any old hardware you put together.

Your best bet is to go onto the XDA forums and see what hardware people are already using and supporting with builds. This will get you the best results. Otherwise you're likely compiling custom builds yourself.

Any android phone from the past 5/6 years, install Lineage, use a USB-C to HDMI Converter that has a charging input (they exist)

The problem is app support for x86. Many just are released for arm and arm64.

At least back when I tried it.

Also, power management on x86 sucks hard compared to arm, so expect much higher power usage compared to an Android stick.

It's a fun project tough....

IDK about the current status of x86 with android, but last time I checked it wasn't good.

Lineage might be your best bet... it supports a few androidtv boxes (most notably the nvidia shield) see https://wiki.lineageos.org/devices/