1998 Honda Civic hesitation

I recently purchased a 96 civic, 1.6l, (d16y8), 4 speed automatic, 94000 miles, I tuned the engine with all honda original equipment parts-plugs, cap, rotor, wires, gas filter, also timing belt, water pump. And im still having this hesitation/power loss when eng is cold. Only for half mile to 1 mile, after that, car runs great. The trans is a 4 speed automatic, I flushed the trans once so far with honda trans fluid, going to flush at least 2 more times. I always believed in oem parts with all my vehicles. I checked the fuel pressure today- was 35psi regulated and 45psi with regulator disconnected. The car has no check eng lights and also checked for codes-none. I have done a complete visual inspection on everything under the hood several times. The car will shift from 1st to second with no problem, then 2nd gear has this hesitation/power loss untill I can get car to 2600 to 3000 rpm, and then it just takes off. Only will do this when car is cold. When the car is warmed up, it runs and shifts perfect all gears. The car will not have another issue unless car sits for several hours. I also noticed twice when eng is cold and idling, it would run rough and almost stall, and then the idle would just jump and then idle normal. Any help or suggestions would be great. Not sure where to go from here. Can really use honda tech's advice. Thanks