Congratulations on your new ride.

It could certainly be a lot of things, but my experience, and from what I have read on the board, says there are very few problems with the engine sensors in these cars.

Do you have any oil leaks? The Distributor os at the very back of the engine block on these cars and oil can leak into the dist cap. This will cause you to run more and more poorly until it will finally make it quit starting. It's a little harder to pull than on the Bosch cars: just three bolts, but it's a little tight. You might want to pull it to check the condition of the cap and rotor besides checking for oil. If you do have significan oil in there, you may need seals, but you probably have a problem with the flame trap (PCV) system you should clear first.

I wouldn't think fuel pump first. I would expect that to be more of a problem when revved up if the pump were failing and I don't see how this would explain the cylindars dying one at a time.
--
Andy in St. Paul. '89 244 153K mi, '91 745 Regina 202K, '88 244 184K