From the factory....
You should have a screen on the pickup tube in the tank, the fuel pump and then the filter, lastly the carburetor and cylinders.
I would start with running the car for about 5-10 minutes and letting it idle. Shut it off and check the fuel pump. If it is a mechanical pump, there should be a weep hole where fuel will leak out of and this indicates a bad diaphragm in the pump.
If the pump is good, change your fuel filter out for a new one, if that doesn't help, check your cylinder compression and timing.
Lastly, rebuild the carburetor. If your bowl to top gasket is still good you can just pop the top of the carburetor off and see if the float is stuck or if there is an excessive amount of deposits in the float bowl which can clog up the jets and what not.
Even after cleaning out my tank and putting a new screen on the pickup, and running it with a fresh filter, I can find deposits in my float bowl on a regular basis.