ESP8266 is a low cost (2-3$ in begin of 2019) WIFI microchip with a 80/160 MHz CPU, which will be used for a lot of DIY projects.
If you are looking for more powerful microchip, or you need Bluetooth capability, check out the successor ESP32.
I bought the “D1 Mini” model of ESP8266 with 4MB flash (you can get them e.g. here).
Note: It is not the WeMos D1 Mini, but a copy of it. The PIN diagram is the same, which you can find here.