based on your description of the problem, i would check the following:
1. accelerator pump, is it giving a shot of fuel when the carb is cold. some times the cup portion of the pump won't work well till it and the carb warms up and it seals better in the chamber.
2. choke setting, too tight and the carb runs rich, too loose and it will run lean.
3. choke pull off or as gm calls it, vacuum break. this device opens the choke plate a set amount once the eng starts and runs. this is set with an angle gauge or sometimes with a carb gauge tool. a carb gauge tool is a set of dowels of various sizes and are used like a feeler gauge to set various gaps in the carb, i.e., choke, throttle plates, etc. think drill bits without the point or flutes. if the vacuum break is set to open too much (lean), it can cause a stumble of stall. set to open too little, (rich) it will cause a stalling and hard restart.
4. lastly but most importantly, get a factory service manual for your make and model. not a chilton but a factory manual. the information contained in one is a gold mine. it will have specs, step by step procedures for setting up a carb and it will have descriptions of how all the circuits in the carb are suppose to work.