...I don't think it is degraded gas. I just filled up not long ago. I will check the fuel filter at the carburetor.
By all means, check the fuel filter. Remove the check valve and blow through it. If there is
any resistance, replace it. But, don't disregard the potential for bad gas. A gas station with water in its tanks is not unprecedented. Did the symptoms begin shortly after fueling your vehicle?
You didn't say how many miles have accumulated since the last tune-up. Check the cap, rotor and a couple of spark plugs. In addition, when an ignition control module or pickup coil fail, symptoms can be similar to those you are experiencing. Checking the ignition using the HEI tester recommended earlier is a simple and effective go-no-go test. Sparks should be blue in color, definite and maintain a consistent, rhythmic arc with engine cranking.
Regarding the longstanding hesitation from a stop, verify that the vacuum advance actually holds vacuum and that it rotates the pickup coil stator inside the distributor when vacuum is applied.