There is probably not much quadcopter build experience here (I could be wrong ) so we're not really the ones to ask but if I were going to build one I would use a 5V, 16Mhz Pro-Mini because they are small and have all the functionality of an UNO, (mostly), the
difference being the need to use and external FTDI BASIC breakout board to upload sketches. In addition, the Mini always comes with the headers so you can choose whether or not to use them. For a quadcopter you would not want to install them and connect only the wires you need. the one header you need to install is the one for the FTDI basic connection on the end of the board. You want to install this right-angle header on the top of the board with the pins facing outward. The FTDI will plug right into it. If you buy a clone instead of official arduino , the FTDI pinout may be reversed (mirror image) requiring you to plug the FTDI in upside down. You need to check the pinout before doing anything.