I would just choose to make sure everything is correct.
The car is 55 years old and the parts used when the car was manufactured only needed to last 5-10 years at most.
If you don't personally know the entire history of this car, don't assume anything was done properly.
Only way is to replace the brake system. Some people will think this is unnecessary but the brake system is the most important system on the whole car and the cost to replace, relative to everything else is minimal. Do it right and you will only do it once.
Remember that "The quality is remembered long after the price is forgotten."
Download a Factory Service Manual and use it to guide you.
Service Manuals – MyMopar
If you can't afford to do the entire system at once, start at the top and work your way down.
Never use rebuilt hydraulic parts, always top quality new.
So first would be New master cylinder and new/rebuilt booster.
Order a complete hard line kit. NO NOT ORDER S/S. Use the factory steel lines.
Replace front brake hoses, new quality wheel cylinders.
New brake hardware and adjusters.
Quality BONDED linings, no riveted stuff, they crack at the rivet holes.
New wheel bearings AND races, seals.
Do the same to the rear axle with one exception, also make sure to replace the body to differential soft brake hose as well.
Drain and flush the entire brake system BEFORE you install any parts that fluid flows through as the crud in the lines will go into the new parts.
Always use new brake fluid from a sealed bottle. Brake fluid is hydro scopic meaning it absorbs water even theorgh rubber lines and whenever you open the m/c lid. It should be completely bled out every 3 years.
Moisture in the lines will led to corrosion in the entire brake system and when the fluid to water ratio get too high, under extreme hard braking the water in the lines will boil off and leave air in the system which is why you lose the brake pedal when coming down a mountain road or heat up the brake system with long or hard stops.
Brake fluid testers can be got from Amazon or any large auto parts store for around $10 for an economy type.