I have used the ProMicro and the nano for a few projects and they are both great boards. I had a little bit of trouble getting the Pro Micro up and running but SparkFun has a great tutorial that should give you plenty of information to get that board up and running. If it's between those three boards, I would suggest the Pro Micro.
You could also consider the Pro Mini (https://www.sparkfun.com/products/11114). You will need an FTDI programmer for it (https://www.sparkfun.com/products/9873) but don't be discouraged by that. It's really straightforward to use. The cost is about the same as the Pro Micro and there are no special drivers required to get your computer talking to the Pro Micro. The Pro Mini with the FTDI basic "just works". One disadvantage to the Pro Micro is that you won't be able to power it over USB unless you leave the FTDI attached to it...but like most Arduinos you can just power it over a pin with a wide range of voltages.
Really any of the boards you mentioned will do the job.
Another board that's even smaller than the ones you mentioned would be the trinket or pro trinket by Adafruit. Similar to the pro micro, you need some additional drivers but Adafruit is really good about providing tutorials.
If you don't want to worry about external programmers and additional drivers and you want to power over usb get the Micro. If you are powering off of a battery and need to wire it up anyway and are willing to do a little bit of configuration on your computer consider the Pro Micro or the trinket.