When you hear a brake squeek, you are hearing vibration. That's it in a nutshell. Now, that vibration can be caused by a number of things including dust, glazing, etc etc. When you get a brake job done, many shops only throw in a set of pads and finish the rotors. That is NOT a complete brake job. To do it right, you must finish the rotors to the specs of the pad manufacturer and bed in the pads and rotors with their exact procedure. Also, a complete brake job also entails replacing all the brake hardware. Without that, you are using worn stuff. If done correctly, they shouldn't squeak. That being said, you can still get the squeak to come back. You can overheat the rotors for example. FWD cars were notorious for noisy brakes. The front brakes were small and over worked with all the weight on the front of the vehicle. But for our cars who are near perfectly balanced, a proper brake job with the correct application of components should yield a nice quiet brake.
By the way...if you go throw hard "racing" pads on the car and expect it to perform like the factory ones did when it comes to squeaking and stopping ability on the street...it ain't gonna happen! They are hard...require heat to operate the way their intended...and in many cases require a specific rotor that will handle the heat.