Arduino Wireless Relay System & Servo Questions

I'm trying to build a beer cannon (haha) out of an arduino uno and various other parts - but I'm having a tough time figuring out the best way to go about it. The idea is for a mobile app to control a mini fridge like a vending machine and drop a drink into an air cannon which you can then fire from said app. Here is an example - Mini fridge beer cannon - Update - YouTube.
So essentially, the arduino is doing 2 things - controlling a servo which releases the cans and then activating a sprinkler valve to fire the air cannon.
In this video, the gentleman is using an I/O bridge module, but I am looking to accomplish this with an arduino uno. Currently, I'm looking at getting a relay to control the sprinkler valve for the air cannon, and then just controlling the servo's with the arduino, but as to making it a wireless system so that I could control it from an app I'm a little lost. How would I connect 1 Bluetooth module and get it to perform these various tasks for me? If there's a better way to go about the circuitry as well I'm all ears, thanks!

Additional information about the project can be found here -

Probably the easiest wireless setup would be to use an inexpensive RC tx/rx setup.