Im leaning towards the electrical, but then again it is somewhat normal for the car to have a lack of power if you instantly start it. as you have noticed when you turn the ignition on and the dash lights up your car starts just fine. your electrical system had enough time to round up the necessary voltage to supply both the starter and spark plugs with the necessary power to start up correctly.
When you start it suddenly you didn't give your electrical enough time to 'wake up' and distribute the energy as it should have.
The above mentioned is what i have come to understand with my own experience and the word of an automotive electrician i know (a bad as mofo at it too).
All the cars i have ever owned wether they be American or import have done the same thing you speak of.
Now assuming something is wrong i would start with the basics. check and clean all grounds in your car. i would lean towards a weak point in your electrical system being the cause. maybe some loose grounds or power wiring. also when you start your car is there any draw on the electrical system? Are the lights on, is the stereo on, are you holding the brake pedal down? Any draw on the system will give you the same symptoms.
His -1996 GT- Steeda underdrive pulleys, SR CAI, SR intake spacer, SR adjustable clutch kit, SPEC stage 1 clutch, RAM steel billet flywheel,magnaflow cat back with pipes cut off after muffles( love the sound), Tokhico rear shocks, Tokhico front struts, Smoked Cobra style headlights & white tail lights for good looks.- nickname = Rolling Thunder
Hers - 1998 v6 convertible - dual exhaust, SR CAI nickname = sexy thang