The ESP-01 model (which I have) has 2 GPIO pins that are useful for stuff. The other models (eg ESP-12F) which have more pins available are a bit larger and look to be more fiddly to use, but I still might buy a couple since they're less than £1.50 each, you can get a mounting board for about 10p anyway.
ESP-01
ESP-12F
To use deep sleep you need access to GPIO 16, which isn't normally available on the ESP-01 (only GPIO 0 and 2). You need to do this...
(and my soldering iron tip is too fat
:C )