Car Idles Low, Sometimes Dies and/or Won't Start Temporarily

I own a 1990 Crown Victoria LTD base sedan with a 5.0L V8. Ever since I bought it, the car feels like it sputters slightly while keeping a constant speed or slowly accelerating in a low idle range. The sputter makes it feel like the car is lurching slightly and occasionally makes a rattling noise in the drivetrain. Now that winter is here, my car began to have more problems. Sometimes when started, the engine roars to life but then dies quickly. Generally after a few tries, the engine will start but will idle very low and not seem to warm up. When I slow down or come to a standstill, occasionally my car will drop to a very low idle and then die. For the next five minutes or so, it won't start, sounding like there isn't any fuel getting to the engine. After about five minutes, the engine will start fairly normally but usually idles too low and sometimes will die again. Do you know what is causing this? My dad thinks it's the distributor but I think it's something to do with the fuel pressure.