In Chinese webstores a “ESP-01S RGB LED Controller Module for Arduino IDE WS2812 Light Ring Smart Electronic DIY” module is sold for less than a dollar (if you buy it without the ESP8266-01). The module contains everything that is needed to have an ESP8266-01S control a Neopixel strip
The module uses GPIO2 as output for the Neopixel(s). Suitable Software can be found here. Make sure you use the new ESP8266-01S with this module. The ESP8266-01S has the necessary pull up resistors already available. If you use the standard ESP8266-01 you need to attach the required pullups yourself.