Lots of interesting advice here, but lets get to basics.
First thing is to do a real, ground up tune-up of the engine. A compression test is pointless unless you have adjusted the valves. I'll post that procedure below. Full tune-up on the carburetor, adjust float level, idle screws, and choke. New wires, new double-platinum plugs, new points, cap, rotor, and condenser. Even better, send the distributor to Dan at the Mustang Barn for recurve. I guarantee it is way out of adjustment now. If there is the slightest possibility that the valve stem seals are bad (as in rock hard or disintegrating) replace them. This can be done with the engine in the car. Unless the rings are totally shot, or a valve is burned, this will get you to Dairy Queen and back for many years to come.
Adjust hydraulic valves with the engine cold.
Do this, and it will run smoothly, and likely with more power:
Disconnect the coil + wire.
Attach a bump switch to the solenoid, or just use a screwdriver.
Turn the engine so the #1 intake valve is fully opened. Loosen the exhaust valve until you can move the #1 exhaust valve pushrod up and down (NOT spinning).
Tighten this valve until no up and down movement can be felt, then tighten an additional 3/4 turn.
Note: Spinning the pushrod can cause a false adjustment, as a slowly collapsing lifter can allow the pushrod to spin freely, thus throwing off the base line of your adjustment.
Turn the engine so the #1 exhaust valve is fully opened. Loosen the intake valve until you can move the #1 intake valve pushrod up and down (again, NOT spinning).
Tighten this valve until no up and down movement can be felt, then tighten an additional 3/4 turn.
Repeat for the other 7 cylinders.
I did this on a friend’s engine that had been adjusted when built, then driven for several years. It was running OK, but not great, you could hear some valve noise. After doing the above, it did not seem to be much better immediately after adjustment, mostly because the lifters had been varnished into position by years of driving. Coupla miles around the block, though, and it was a whole 'nother engine.