Which Arduino board to select for designing a Quadcopter?
The right board for you is the board that best fits your design.  Leave the Arduino as a "black box" in your design and don't worry about it.  Once you know what you need from your Arduino board in the way of control interfaces, IO, processing power, etc, you (and we) will be in a better position to choose a suitable board.

Until then you're basically asking "I want to take my driving test. What kind of car should I buy?", which makes absolutely no sense.