The MOST likely source of your issue is either the IAC valve, ot the ECT sensor (Engine Coolant Temp).
The rest of the "possibilities" you mention, would NOT show up for a cold start only, and would not cause the symptoms you describe (having to feather the gas to keep it running).
However, you could very well have a vacuum leak, and even a small vacuum leak *can* under some circumstances, prevent a decent cold start.