Picked up a 66 Galaxie 500, has an issue with the brakes that feels...i dont know, weird.

There is about 1/2 to 3/4" from when I apply pressure to when it is solid and I cant push it down further. In that short pedal distance it engages the brakes and stops the car but it obviously isn't right and feels so odd that I have to find out what it is and fix it.

I cant figure out how else to explain it other than I touch the pedal, put pressure on it, hard or soft, and it stops the car. There is such a short amount of travel its odd...but it doesnt lock up the brakes, it just brings the car to a halt. It feels like something is broken, not working right, I dont know. Anyone here know what I am trying to explain?

 

A thorough inspection of the entire brake system would be a good place to start.
Don't know what kind of maintenance the vehicle had so gotta start from scratch.
Among some of the possibilities would be , frozen wheel cylinders, weak brake hoses possibly ballooning.master cyl cups leaking. As you can see there are quite a few places to start. Rusted brake drums with not enough stock to do the job. Let us know what you find.