If you want maximum number of LEDs, I think you want the four-wire LED strips that are driven over SPI, like the APA102 and similar. Much faster than bit-banging on the three-wire strips.
You can find how to control them if you search for HUB75. For a couple of dollars you got 2048 LEDS. You can get them in different sizes and LED pitches.
https://www.bhencke.com/pixelblaze
This page seems to have more information about a couple of different methods - apparently it's also possible to use a UART peripheral:
https://github.com/Makuna/NeoPixelBus/wiki/ESP8266-NeoMethod...