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That's how I do it, Bluetooth controller, wifi for sync and just a RPI with power and HDMI.

The bluetooth module in built-in on RPI 3, you can also use a cheap Bluetooth adapter for PC, it works too.

When the controller's battery dies I just play chill games like pokemon with my phone as a controller (RetroArch feature "Remote Gamepad") and keep going.

You can plug you PC or laptop to the TV in the meantime. 😎