You have some great goals.
Set them aside.
Start with smaller, incremental steps.
Have you run the Blink tutorial? This lets you know that you can hook up the arduino to the computer, push up a sketch and see the arduino run your code.
Next, run the sweep tutorial (if your solver will use RC hobby servos)
Next, work on whatever connectivity your mobile application will use to interact with the arduino.
We can help you with this as you try each step and if you have questions along the way.