engine stall/lack of fuel

This is the first mopar ive ever owned and, frankly, the oldest car I have ever owned, so please forgive me if this is a simple problem.

My 1970 Valiant tends to stall driving around town when the accelerator pedal is pushed lightly. If I push hard on the pedal, though, the car accelerates and has no problems. Also, after coming off of the interstate, and coming to a complete stop, the engine will die altogether, requiring me to put it in park, pump the gas and restart. While idling too longer, the engine sometimes dies, as well, but not at higher speeds, such as intersate driving.

I checked the automatic choke, and that seems to be fine. the fuel lines also look good. What might be causing this? I am assuming it must be something with the holley carburator, and I may need to get a new one.