Which board to use for wireless communication of small packages?
WiFi round trip time is about 2-50 ms (50 is the worst case), so, you can use the ESP's and the UDP/TCP.

On the other hand, you can use the NRF433 module, but in this case, you have to develop your own channel level protocol, with error detection/correction and so on.

Also, there are ZigBee module. They developed for home automation specially.