Strategy for Remote RPi integration?

I would like to install the HA in a Intel Nuc computer and use a remote Raspberry pi with some GPIO expander boards to control all the house inputs and outputs.

I read this guides:
https://www.home-assistant.io/integrations/remote_rpi_gpio/
https://gpiozero.readthedocs.io/en/stable/remote_gpio.html

And also:
https://github.com/flyte/pi-mqtt-gpio

I don’t know how to start. In the pi-mqtt-gpio I saw that is prepared to work with GPIO expanders. There is an example of that.

Can someone explain, step by step, how to install that in the remote pi? And how to prepare HA?

remote_rpi_gpio is different from pi-mqtt-gpio? Right?

Preparing the remote Raspberry Pi:

Step 1 - Install Raspbian
Step 2 - Install the PI MQTT GPIO
pip install pi-mqtt-gpio
Step 3 - ??

It’s correct? What to do next? Install mosquitto?