Make sure you hear a click at the carb. when you turn the key on, and another when you turn the key off. If you don't, then most likely there is a problem either with the fuel shut off solenoid or the wiring to it. If you do hear that click, then pull the fuel line off at the pump, pull it down as close to the ground as you can get it and let it drain into a gas safe container. If no fuel comes out, then chances are there is a blockage in the fuel line. How much have you cranked on the engine since you changed the fuel pump and filter? Are you certain you don't still have a large air pocket in the line?
There is no fuel in the fuel filter or carb. Fuel has to be drawn out of tank by the pump. You bring up a good point - do I need to prime the system - too much air in it now?
There is no blockage, new filter, new pump, clean cap.
Does the fuel shutoff solenoid click when you turn the key switch on and off? If it does, then that may not be the problem. It does have a new filter and pump, but what about a possible blockage in the fuel line or tank itself? You can test for fuel flow by disconnecting the fuel line at the pump and putting the open hose end into a safe container, then using your hand and an airline to gently pressurize the fuel tank. If gas runs out the hose, then all is good up to the fuel pump. If not, then you have a blockage. Not exactly a precise test, nor a safe one if you're around a source of ignition, but one best performed out in the yard in a very well ventilated area. If you do have fuel flow, then just move down stream to the pump. Make certain the new pump is working. The vacuum line that operates the pump should have a "pulse" feel to it if you put your thumb over the end of that hose while you crank on the engine. If that checks out, then you should be getting gas to the carb. If after all this you are getting gas to the carb, then you may need to clean the carb out.
Since the engine runs when you put gas into the line, the fuel shut off solenoid is working. It is possible the new pump is bad. However, you mentioned the line from the tank to the pump is clear....how did you determine this? Also, are you certain you have the fuel filter installed the correct way. There should be an arrow on it somewhere showing which way the fuel should flow.