Would this be the right one to buy for Home Assistant Yellow with Power Supply?
That is a stand-alone Raspberry Pi.
you need a Raspberry Pi 4 CM module
https://www.raspberrypi.com/products/compute-module-4/?variant=raspberry-pi-cm4001000
Thanks. Everywhere seems to be out of stock
That one will work.
That is for you to decide. The Yellow has an Ethernet port, so you don’t really need wireless.
Personally, I would highly recommend going wired over wireless. Wired is going to give you more stability. Plus, if you get a PoE HAT for your PI and have a PoE switch, you can run the power off your switch and then you only need to worry about putting you switch on UPS.
I am doing this in my home. It is just a network wire to my PI 4B 8GB up on a shelf with the Z-Wave and Zigbee radios on it. No other wires needed. Very clean install and very robust.