Possible coolant temp sensor? If the engine computer thinks it's warmer than it really is, it will not command a sufficient priming squirt from the injectors. Look for the two-wire sensor. The single-wire temp sensor is for the gauge on the dash. Chrysler doesn't have much trouble with temperature sensors; Ford has a lot.
Also possible low fuel pressure or the pump isn't starting right away. GM trucks won't run at all if the fuel pressure is just a few pounds low. Dodge trucks will run, but may develop problems such as yours.
If fuel pressure is bleeding off while the trucks sits for a while, suspect a leaking injector. You can prove this by cycling the ignition switch on for a few seconds without cranking the engine. Turn it back of, wait five seconds, turn it on again, and maybe do this a third time. Every time you turn it on, the fuel pump will run for two seconds, then stop until the engine computer sees engine rotation, (cranking or running). These two or three bursts from the pump will insure pressure is up and ready for starting. If it starts right away now, an injector is leaking, or the pressure regulator or pump check valve is leaking. I think by 2003, your regulator is in the tank, not on the fuel rail on the engine. I would just live with those because of the cost of a new fuel pump assembly, but if it's a leaking injector, raw fuel will be dumped into the intake manifold after you shut the engine off. The fuel could run down past the piston rings into the oil, reducing its lubricating properties. This isn't quite as critical if you do a lot of long trip driving, like 15 - 20 or more miles. Long trips with the engine fully warmed up will tend to vaporize the fuel in the oil. It will get drawn out through the PCV valve and burned.