I would not have thought that shields of any sort were the way to build your own quadcopter. They will be relatively heavy and expensive. I would have thought a better approach would be to use one of the Arduino clones designed for the purpose, which integrates the IMU onto the controller board and uses external high power motor controllers to drive the motors. Brushless motors seem to offer a much better power to weight ratio if you can afford them, in which case you'll need the corresponding controllers.
Unless you particularly want to develop a complex sensor analysis and control algorithm from scratch it would also be sensible to adopt a working autopilot that is compatible with the board you're chosen.