Gritty and bad brakes. Trying to troubleshoot
 

I recently bought a 1995 Ford Mustang GTS and the brakes are pretty bad.
Brakes and rotors look fine and don't need changed, but as I step on the brake pedal it gets to it's normal point and slows the car down a bit but then I feel a grinding almost gritty feeling in the brakes and then the brake pedal sinks to the floor and finally stops. Seems to do it everytime i brake to a stop but doesn't do it until i'm almost to a complete stop. Going to try n bleed the brakes but does anyone think this could be a booster or master cylinder problem?