anemometer project using wifi

I am looking to start an anemometer project with my 10yo daughter. We have an Arduino Uno and an IR sensor. Plan is to use the sensor to measure rotations and calculate the wind speed from there.

Ideally, I would love to get the data off the Arduino to a database. Originally I thought perhaps store on an SD card then somehow get the data from there, but have noticed the ESP8266 WiFi module. Am I right in thinking I can use it to repeatedly throw post data at a web page? I am comfortable with PHP/mysql, but very new to Arduino. Also, would the ESP8266 and the IR module both run off an Arduino Nano if we needed to scale it down to save space? Thank you for any advice.

You can indeed use the ESP module to talk to your database over wifi. Better still, it will have some (varies by model) GPIO, so no need for a Nano, it can do the whole job by itself.

ESP32 and ESP8266, 32 bit models running at quite some speed and capability over an Uno being controlled by an Uno, why not get a ESP8266 or a ESP32?

I have an ESP32 I used to build a weather station. Inside the house I have a Raspberry Pi running as my MQTT Broker. Weather data is sent to the MQTT Broker where the info is transfered to various locations, one being my web site.

Oh perfect, thank you both. Even better if it can run on its own and just talk to the router.