I have been driving this car for 12 years with NO problems to speak of. It always starts right up no matter what the weather or temp.
Three days ago it started hesitating when I started out from a stopped position. Then it stalled out completely after a minute or so…no weird noises or bucking…it just died - quietly.
It always starts up again immediately. It will drive fine on a straightaway without any problem - until I stop!
I have been remiss about maintenance since this car is used only as a local run-about (grocery store, garden center, library: all within a 25 mile area).
Is it the fuel filter? Or some simple thing like that?
I want to keep this car until it is absolutely beyond help!!! (Yes, I am probably a lunatic! 
Sure, change the original fuel filter. And air filter, just to be sure.
The next suspect is the ignition module. And, the ignition switch.
I’m not laughing. There’s nothing wrong with a '97 Escort. They are generally extremely reliable cars, as yours has been. My cars are 12 and 13 years old, so I have nothing against your car because of its age, either.
You haven’t told us the mileage on this car, and if we knew that we might better suggest the cause of your car’s problems. Regardless, ignoring maintenance is a good way to turn a reliable car into an unreliable car, as you are now discovering. This is false economy, and ends up costing more in the long run.
Short local trips are the hardest life a car will ever live. Your car’s life would be easier if you drove it 100 miles on the highway every day. You should be following the “severe service” maintenance schedule.
I suggest you make an appointment with your mechanic to have ALL maintenance items brought up to date. The car may need spark plugs, a fuel filter, transmission fluid replacement, etc, depending on mileage. There should be a maintenance schedule with the owner’s manual that will tell you what is required.
Pay particular attention to the replacement interval for the timing belt (aka camshaft drive belt). Your Escort has what’s known as an “interference” engine. If the timing belt breaks the pistons and valves inside the engine will collide, causing significant internal engine damage, and the cost of repair will make you very unhappy.
Bring the maintenance up to date and continue driving and enjoying your Escort for many years to come.
Please tell us how many miles are on the car now.
It’s probably minor in nature. It sounds like either a vacuum leak has developed (easily verified with a vacuum gauge) or the Idle Air Control valve is acting up.
If your engine stalls when you come to a stop, it’s likely that you have a faulty Idle Air Control valve (IAC).