Over the next year, I along with a few friends are going to attempt to develop a quad-copter with a 3D printed frame for school. We hope to use an arduino micro controller because of its capabilities but we (and also our teachers) are unfamiliar with arduinos and don't know what to buy for this build. The idea is to have 4 DC motors on each end of the quad-copter connected in the center by an arduino board which is controlled either by Bluetooth from a smart phone or by a radio transmitter/receiver method from a model aviation controller. If anyone has any advice on which arduino to use, which DC motors to get or which method for wireless control we should use, is greatly appreciated.
I'll just point you here
You need more than just a microcontroller to maintain stable flight on a quad. Minimum is a gyro and an accelerometer and a PID loop in the code. You also don't mention ESC's but you'll need them too with some brushless motors.
You could probably run standard brushed motors but they may struggle with torque.