If you choose to go with the small one (see previous image in post #5), then there's enough space for a Nano or a Pro Mini. Get the 3v3 version so you can run directly from the battery.
It'll probably take one of the Adafruit Feather boards with a built-in radio module.
You should look for a board that has a built-in radio module as there's just enough room for 1 daughter board or a small collection of hard wired sensor boards.