First off, hardware:
I am using a Raspberry Pi, SD Card, power supply, WiFi adapter, keyboard and mouse, HDMI Cable. Optional is a case.
In my configuration I have the Pi mounted on the back of my main TV in the center of the house. I used a wireless keyboard and mouse.
The Pi, it doesn't make sense to use anything except the 3, unless you have one hanging around and not using it for anything else. Some people have talked about the Pi Zero but I have not used one and I think having no USB ports for WiFi and Keyboard/Mouse would be a problem.
I shopped around and got one of the better Class 10 major brand SD cards. I tried Samsung, Sony and Toshiba. I did not notice much difference between any of them but the Samsung (80MB/s) was rated twice the Toshiba (40MB/s) read time. I think that the Pi I\O on the SD Cards are just rather slow. The price difference is not much so I would recommend the Samsung or other brand name cards in the area of 80MB/s.
You will need a good power supply. When I started with the Pi, many (it seems) years ago there were many things that caused a crash. After many hours of trying to figure things out I swapped out the power supply and cable and most of the ghost left the house. I recommend getting a power supply specifically for the Pi and not the cheapest as this is going to be running 24/7 and in control of your home.
The Pi 3 has builtin WiFi but no external antenna and I have not heard much good about it. The Access Point drivers are maybe a bit iffy. I tried many WiFi Adapters and all caused much grief when trying to setup in the AP Mode. We will be using the Pi as a WiFi Access Point for all our devices. The only WiFi adapter I got working and found documentation on setting it up that actually worked was the one from Panda Wireless, I got the one with the external antenna for better coverage. The PAU 06.
The keyboard and mouse will not be used much after initial setup so a $20-$30 (or less) on sale set should work well.
The last required item is the HDMI Cable. I found a 18" one at the dollar store. It worked and I am not too sure why the same length cable at the 'electronics store' was $12.95 but this one works, is never unplugged and plugged again, so I guess it's good enough.
The optional case. I got the most minimal that included a fan. I think the fan actually cost more then the case but it seems to be a good one, with ball bearings and is very quiet. After all, I put it on my TV and would not put up with fan noise while watching TV.
Well that's the list of stuff to start collecting for now. I hope to write the next chapter fairly soon, so stayed tuned.