When I first apply the brakes I hear this impact sound, like something snaps.

It doesn't matter if I press the pedal softly or firmly, same sound.

Any ideas as to what it could be and how much to fix??

TYIA,
Will.

 

You can check for the easy things first. Make sure all the wheel lug nuts are torqued correctly, 80 ft-lbs or so. Make sure the brake caliper brackets (the torque member, not the caliper) are secured to the wheel hub. Also, is this front or rear? Would it make the noise if the hand brake is pulled? Jack up each side of the car and see if the wheel is wobbled.

 

upper strut mounts are shot. Replace both of them