Welcome to the world of aftermarket hydraulic lifters. I have a '53 full pressure 235 which has 10,000 miles on it and does exactly what yours does until it reaches operating temperature, then runs as quiet as a mouse. It has done that since it was rebuilt. I was hoping that it would go away, but it has not. I just let it run at idle until warmed up and live with it.
The issue with fuel delivery: Tell us about the fuel tank. New? Thoroughly cleaned? Don't know?
Pull the fuel line from the carburetor and put a rubber hose on the end of it to go into a Diet Coke bottle and turn the engine over with the starter with the ignition off. You should get some pretty decent spurts of gas going into the bottle in just a few revolutions of the engine.
If you do not need to ever use the choke to start the engine, you are running too rich at idle. Adjusting the idle/mixture screw may address this.
Pull all of your spark plugs to see what they will tell you. They generally speak volumes. Dry black soot will indicate too rich.
Carl