How does the ESP8266 relate to the device you link to? It looks like it does the job for you.
What have you come up with yourself?
What is your experience with WiFi programming? MQTT? Embedded app development in general?
How frequently are you updating the MQTT data? How will the device be powered and how easily can it be accessed to replace/recharge batteries if that is the source?
Will the ESP8266 be expected to do anything else in between taking the samples and sending them on?
Susan