99% chance this ISN'T it...but...
My '96 had the typical (especially for that year) ECM capacitor leak problem. If I started it up and just drove off, the first chance I had to let it idle (stop light, whatever), it would run like shit and die IF I didn't keep it revved above idle with the pedal. It might be 200 miles later, but the first chance I'd give it to just idle on its own, pffff. Your symptoms.
Eventually, I stumbled into a workaround: When first starting it, I had to let it run until it dropped down from "high" idle (not necessarily cold-weather-high-idle, just until it settled...) before driving off. And this was a 5-speed. After its idle stabilized, until I shut it off and re-started again it would run like a goddamn top, idle fine, 30mpg, day in day out. Start it, wait a half a minute until the idle settled, then golden. Most bizarre thing I've ever run into automotive-wise, but stone cold reliable.
Try that. Otherwise, I got nuthin but loads of random guesses.