The board design and code has been tested using an Arduino clone commonly referred to as the "Pro Micro". It is not an official Arduino design, but was developed by SparkFun - it is basically a compact Arduino Leonardo with a few pins (11, 12, 13, A4, A5) missing. It is based on the Atmel ATMega32u4 USB-enabled microcontroller. Since it is a Leonardo clone, it uses the same (Caterina) bootloader.
To all intents and purposes, you should be able to treat it like an Arduino Leonardo (with the exception of any use of the missing pins - but obviously EDTracker doesn't make use of them)
"Mini" and "Nano" versions are NOT suitable as they use the ATmega328P microcontroller and a separate FTDI USB chipset. Check the data sheet for the device you are considering. If it says ATmega328P or FTDI USB, then it will not work.
If you want to use our PCB, then you specifically need the 24-pin SparkFun Pro Micro. If you're building it into your own PCB solution, then you can choose anything that meets the criteria above.