This project can be done with any Raspberry Pi, but for the most adorably compact version we're using a Pi Zero W - this has enough power to do what we want, and has built in WiFi too!
Its easiest if you pick up a Pi Zero W budget pack as it contains most everything you need
But you can also just DIY with the minimum requirements:
If you are using a Pi Zero W you'll need to add 2x20 headers too
Instead of a Pi Zero W you can directly substitute in a Pi 3 which also has built in WiFi, you won't need the 2x20 header in that case