When the motor is cold it idles fine and revs fine when the accelerator is pressed. When in gear and I press the accelerator the truck drives but sputters and lags a little until the motor is at running temperature then runs like normal. Could this be a fuel system problem or something else?

 

I'd do a modern tune-up on it. Plugs, coil, wires, distributor cap and rotor, fuel filter, air cleaner, PCV valve, ect. If it runs fine after warming up, your fuel pump might be okay but would not hurt to check the pressures. I hate changing fuels pumps, installed in the tank.

When I was a young man we had carburetors with the fuel pump on the front of the motor. It took about fifteen minutes to change them out. Of course, engine fires were more common with the cheap fuel hoses they used back then, but 12-16 PSI was normal, as it didn't take long for the float bowls to stay steady.I believe 16 PSI is normal if you have a TBI. If it's direct fuel injection, then around 60 PSI is normal.

 

i had a similar issue with my 94’ although mine idled ruff when cold as well. it turned out to be the engine coolant temp sensor

 

Interesting. I would not have thought of that. Good work!