Those boards are standalone wifi or can connect to existing networks..
usually used for accessing a 'menu' of sorts.
The reality is you are -not- going to find a plug-n-play solution that fits your needs here..
You will NEED to participate in the creation if you want the control you expressed.
As
Riceball mentions.. your best best is an Arduino.
Also.. you should really spec out your needs here..
And image is 'nice'... but doesnt really help much in terms on:
* LED count
* What LEDS need to be 'animated' (controlled).,
* What LEDS are just 'on' the whole time..
This will help dictate HOW you can control then and the power (current) needed to power it all.
An Arduino and MAX7219 chip can control up to 64 leds (each MAX chip, which can be daisy chained together to control more if needed)
An Arduino and Neopixels (WS2812 leds) can be be individually addressed and controlled for color & brightness (usually a bigger current need)