Let me ask u this:
When u start the car, are u turning the key from the off position to the start position right away? Or, do u turn the key to On, let the fuel pump pressurize, and let the sensors "warm up", before starting?
The reason I ask is because this little detail is the difference between nice smooth running after starting, and the EXACT symptoms u describe in my GF's 96 Zetec Tour. Although the problem with her car won't happen every time.. theres been instances where I've gotten in the car, started it up forgetting to do the key trick, and had it start stumbling and missing/trying to die on me. The times this has happened I've killed the engine right away before the computer could throw a CEL, then turned the key to ON, let it sit for a few seconds, then moved the key to START and had it run perfectly, just seconds after it ran like total crap!!
I have cleaned this cars MAF sensor which seemed to help tremendously (this also singlehandedly took care of a pinging issue the car had).
My theory is all our MAF sensors are dirty and less accurate as the mileage gets up there... ESPECIALLY if you've added an aftermarket intake with an oiled filter.. these are known for gucking up MAF sensor filaments. I think the MAF sensor works by heating up one or both of those wires. The air coming in does something with the resistance in the wires and the computer can tell how much air is coming in. You can imagine if this part is dirty or just too worn out, its going to cause problems. The reason you're getting a CEL is because the engine runs like crap for a little bit and trips the lean code.
If I were u, I would disconnect the battery, clean the MAF sensor carefully, re-install the MAF, connect the battery, see if it's improved.. if not, do the key trick that I mentioned before.
Good luck!