Q: Do I need brakes or rotors? I was told I needed rotors and a wheel alignment

This may be a sign of warped brake rotors. As you may know, when you press on your brake pedal, this activates a hydraulic pressure which forces small pistons inside your brake calipers to push the brake pads against the brake rotors which is what causes the stopping power you are familiar with. When this happens, an enormous amount of heat is generated due to the friction between the brake pads and rotors. As the brake rotors eventually cool down and then heat up again, the next time you press on the brakes, over time this can cause them to warp slightly causing very small low spots on the surface of the brake rotor. When this happens and the brake pads are applied again to the rotors, this causes an uneven surface (on the rotor) to be applied to the flat surface brake pad, which is what causes the shaking or vibrating you describe. If you would like to have this taken care of, I recommend having a certified technician diagnose the brake system and replace the rotors and pads as necessary.