I created an artificial thunder cloud with individual controlled LEDs to created the lightening and an arduino.

I want to create a updated version were it can play the sound of the thunder but can also be controlled by a wifi or bluetooth remote control or my phone. What's the best device that could do this without costing too much?

 

ESP8266. It's a super cheap wifi-enabled microcontroller that you can use as either a dedicated wifi module, or a standalone device.
It's big brother replacement, which is going to be released shortly, will also have bluetooth, so keep an eye out for that.

 

Raspberry Pi 3?