audio-video via an AVR

I think this is the simplest way to design and connect your system. All the data travels from the media box via AVR that is passes it through to TV. AVRs have multiple HDMI-in ports.

If AVR is connected to any eARC/ARC HDMI ports in the TV, it will also accept the sound from the TV (built-in apps, public TV).

I would also say it is also the most „economic” way of building your system because you could expand your system to match your needs (you can start with a stereo 2.0 set and get into 7.2.1 over time)

This solution should allow to connect all your HDMI devices into a single AVR box and then connect your TV with a single cable which simplifies installation of your TV set (you could achieve a similar effect with an HDMI switch).

Some AVRs can also split a single input into multiple outputs so that you could use a TV and a projector without reconnecting any cables (you could achieve a similar effect with an HDMI splitter).