Guidance & Info about Quadcopter Project
There's a number of parts to this question; there are definitely homebrew quadcopter forums which might be better informed on the mechanical construction details, especially relating to motors and propellors. The item you haven't mentioned is the battery, which is critical to weight and flight time.

The use of ESCs is because the microcontroller cannot drive the current requirement of the motors directly.  Doing your own PWM-based motor control is not too hard; it doesn't even need to be closed-loop speed control. The flight control loop should be built around accelerometers/gyros.

Pi: can run Matlab directly on board, but has hefty power consumption.

Arduino: plenty of people have done it with Arduino, google tells me.

Matlab-to-C++ will not relieve you of the need to write glue code to drive various things. I wouldn't attempt this unless it was something I was very familiar with. You don't need matlab to do simple PID &amp; Kalman filters, etc.

I'd strongly advise getting one of the open programmable quadcopter kits first (e.g. crazyflie) just to get some familiarity with the field.