When I created this board I had the Attiny85 in mind as the Attiny85 has a very nice 8 KB of flash for its small pin count, but it also works with the Attiny45 and Attiny25. It should also work with the Attiny13/13A but it doesn't have PWM available on PB4 so if you want to send a PWM signal to the on-board LED, you will have to remove the jumper and hook the LED to another pin.

So why would you want to use one of the lower-end Attinys? Price. If you plan to make a product that uses an Attiny that you plan to produce a substantial quantity of and your code is able to fit within the 1 KB of flash/64 bytes of RAM of the Attiny13A it looks quite appealing as the Attiny13A can be had for ~$0.60 USD or less if you shop around.