This blog post from our friends at Hack Reactor will be of interest...mostly for the team's contact information so you can learn from the creators.
Answers to your questions/things to think about for the project's design:
Start with the size and desired run time of the quad. These will govern the motors you choose, which will in turn help you pick the proper controller and battery. It will also likely push you towards/away from 3DP vs. a kit for the frame.
Most small quads use tiny brushed DC motors geared down for torque, while bigger vehicles use larger, heavier, and more expensive, but much more powerful brushless DC motors.
Brushed and brushless DC motors require different types of controllers, but my vote would be for any controller that can take a standard servo/PWM/"RC" input as a control because it will interface elegantly with the Servo Module. Ultimately, the controller you should use will depend on the motor technology, peak expected motor current, and battery voltage.
Be careful with the props; in order to cancel out motor torques, most quads have two sets of counter-rotating blades, which means that they carry two sets of propellers that are mirror images of one another.
You'll need an accelerometer as well as a gyroscope and likely a magnetometer if you want any hope of having a quad balance itself. Read: you cannot integrate acceleration twice to get an accurate position (or even once for velocity) because real sensors are not perfect. Any gyro/megnetormeter/full on IMU breakout board from Adafruit/Sparkfun is probably fine so long as it's compatible with 3.3V logic.
That said, you might consider grabbing something like an Ardupilot (which would handle all the sensor fusion/control algorithms and motor commanding) and have Tessel send it high level commands.
Let me know if any of that was unclear and keep the questions coming!