Sounds like there could be multiple problems.
The best approach is to do some basic diagnostics.
First, be ready to catch it in the act. When it won't start, or misses badly.
Several things to check. Look at the plugs. An oil fouled plug will be crusted or sometimes just a piece of carbon across the gap, usually gummy sticky black if it's been run fouled. Cleaning or replacing the plug will be a temporary fix until it fouls again.
This is the type problem that is fixed by doing a ring job or an overhaul to stop the oil getting by the rings.
But, don't jump into doing an overhaul until all other possibilities have been covered. Other things can cause plug fouling, such as weak spark, low compression, open or missing thermostat, rich mixture, short runs/light load/excess idling, over filled oil/gas contaminated oil, leaking head gasket, or restricted crankcase vent tube.
Let's look at the ignition system. Check the points condition, check the gap, check for side play in the distributor shaft. The shaft needs to have very little side movement, otherwise the points will not stay set. Check the centrifugal advance. The rotor should turn a few degrees CCW, then spring back when released. If it's frozen, or doesn't return, the distributor will need to come out, be taken apart, inspected, lubed, repaired as needed. Finally, check the spark quality at the plug end of each wire. Cranking or running, each wire should give a blue hot spark that will jump 1/4" to ground.
Check the compression. If it misses badly after sitting, could be coolant getting into a cylinder. Coolant in a cylinder will stick the rings, stick a valve open, wet the plug to the point it can't fire even with compression. A leaking head gasket will also cause overheating, mystery coolant loss, water and excess vapor out the exhaust, blowing coolant out the radiator. The oil you see around the head, chances are the oil is running down from the valve cover gasket. The only oil pressurized through the head gasket is at the very back, the port for oiling the rockers.
Service the air cleaner. Up inside the canister, above the oil cup, there is a wire mesh that needs cleaning. It is often overlooked. The mesh is difficult to remove and usually easier to replace than try to save if it is heavily caked with dirt, and they usually are.
Check the fuel system. There is a drain plug in the bottom of the carb. With the fuel valve open, have a clean glass ready, remove the plug, catch the flow. It should have a full stream, not slow to a drip or stop. Look at what is caught. If it's dirty, rust chunks, cloudy with water, or water in the bottom of the glass, the tank is contaminated and will need to come off and be rinsed out. If it is flaking rust it maybe time for a new tank, very common at that age.
The same contamination will be in the carb. easy enough to take it apart and clean it, but until clean fuel is supplied, it will get right back in there. Inline filters do not work well with gravity fuel systems.
As for adjusting the carb, that will be the last thing to do. Everything else needs to be done first. The best carb will not overcome other problems with the engine or the ignition system.
Adjust the idle first. The engine needs to be up to operating temperature. The idle speed must be down around 450 RPM. Turning the idle adjustment screw(the small screw up top) in, will richen the mix, out will lean it. The screw adjusts air bleed, not fuel. Back it out to rough idle, then back in to best idle.
Then go to the main adjust. Turn it in to gently seat, then back out 2 turns. Again with the engine up to operating temp, idle the engine down to 450, then suddenly open the throttle, listen for the response. The engine should take sudden throttle without hesitation. Start turning the main jet in 1/4 turn at a time, repeating the test until the engine falters on acceleration. Then back the screw out 1/4 turn at a time, repeating the test until the engine takes throttle without hesitation. A single puff of black smoke is desirable.
This will give you a start, let us know what you find.
