It would help if you told us what engine your Jetta has (I think it could have had a 4 cyl with 8 valves, a 4 cyl with 16 valves, a diesel a V6, & maybe even a turbo 4), and the miles on it and the transmission type - automatic or manual.
The limp gas pedal likely means the pedal linkage has come apart - so make sure that when the pedal is pushed down, the throttle valve opens. Do you have a service manual on the car? I think the manual published by Bentley covers your car, and is the best non-VW manual. The Haynes and Chilton manuals leave a lot to be guessed it as to the electronics of the fuel injection and the bank of relays below the dashboard.
I think the rough idle and the stalling when accelerating are either a lack of fuel or too much air for the amount of fuel. On my 90 Jetta there is a large rubber air duct running from the passenger side of the engine bay back to the throttle valve on the intake manifold. There is a mass air flow sensor in the air filter housing. This along with the manifold pressure sensor is what the computer uses to decide how much fuel it should squirt in via the injectors. If that rubber ducting is loose or has a crack or tear in it - the mass air flow sensor will be sensing less air than is really getting to the intake manifold, and the car will be running very lean. Lean enough to misfire a lot. There is also a rubber tube involved in connecting the idle air control valve to the intake manifold. If that tube is damaged or torn - the air leak can cause misfiring. I believe that once the engine is warmed up, the idle air control valve stays shut, unlike lots of American brand cars where the idle air control valve also controls the 'hot' idle speed.
Of course it could be a low fuel pressure situation. Does your car have two electric fuel pumps? One would be inside the fuel tank, the other one located under the car, below the rear seat. If it has one under the seat, it does have two - since there would be one in the fuel tank in any case. If the pump inside the tank quits working, the car will still run, but might be harder to start and tend to stall often. There is a fuel filter by the pump that is under the car, below the rear seat, but I wouldnt try to change it until you established that there was a fuel pressure problem. I consider it a fair amount of trouble to change - and not damage any of the hoses to it. With the car idling, you should be able to hear and feel that pump running. And by taking the gas cap off, you should hear the pump inside the tank running. Its not a loud noise, or shouldnt be anyway.
If you do a google.com search for 'images', using the search words "+jetta +engine +1988" you might find pictures of what your engine bay looks like, and can tell us the image link. I have a jpeg of the engine bay in my 1990 I could provide, if you sent me an email address. I dont think its possible to post pictures on these forums. I could also upload it to
www.photobucket.com now that I think of it.
Sorry I didnt find your posting sooner. I havent been checking the jetta forums much, due to lack of activity on the older models. I actually have two 1990 Jettas, one of which needs its tranny rebuilt. Im a hobbyist, so will eventually get around to doing that.