Totally shuts off.....
Does it start back up and then die (foot off accelerator)?......if so...try holding the accelerator down slightly....does it start and stay running?
If so....likely cause is Idle Air Control (IAC) valve.....known for sticking....spray some SeaFoam or similar spray lubricant for engines into the small IAC opening (look for other posts here about IAC).
If it shuts off and does not restart at all.
As mentioned MANY things can cause this......weak battery, dirty battery cable connections (on battery terminals and also at starter).
Don't forget the ground connections.....they are just as important as the power (positive) connections.
Intermittent (loose/dirty) electrical connection can cause exactly the problem you are having.
This can be a physical wire connection or a defective battery or a defective relay.
Bad "new" fuel pump.......but along the lines of fuel.....the computer does NOT monitor fuel flow or fuel pressure, so you will not get any trouble codes for this.
One thing that 1999 Windstar has been known for is the fuel pump relay in the relay box in the engine compartment. Not expensive fix. Relay can become intermittent in operation.
No fuel....No run.....engine will not fire at all.
Intermittent fuel issues are mentioned in posts here for 1999 an newer....
Problem with intermittent issues.....is just that....they are intermittent, and since the added problem of fuel flow and pressure not being monitored means that you will not have a failure code indicating a fuel flow or pressure issue stored in the computer.
Fuel pressure can be checked at the fuel rail (I recommend you have a mechanic do this for you as you mention not being handy).
There is a fuel pressure check point at the center of the front fuel rail....easy for your mechanic to do with a fuel pressure gauge.
Problem is.....to have this check done WHEN the vehicle is not able to start......when the problem is happening.
Ignition coil.....normal issue with this is misfire......We have not seen posts of folks having this item cause the vehicle to not start at all (though there is always a first time). so I would not look there first for this problem.