Controlling ESC with Arduino
I 've been working on an autonomous arduino quadcopter for about 7 months now and I have a few tips for you.

1) your setup seems fine as long as your motors aren't going to draw more amps than your ESC can supply, but It is always a good idea to buy ESCs with a higher "max amps" than your motors draws. I would choose 25 amp max ESCs or higher.

2) In order to control the motors via PWM, I use the Servo library because you get a resolution from 700-2000 as opposed to "analogWrite" which gives a default resolution of 0-255.

3) your ESC probably has a minimum pulse width value before it will start. I would recommend writing a program that gives you the ability to plug in values from 700-2000, and use the program to slowlly find that arming pulse width value. Mine is 1110 for reference. 

If you have anymore questions, I will glady answer them. 

May I ask, what is your project?