Clogged fuel injectors?

2002 VW Jetta 1.8 Turbo w/ 103k miles. In the morning, when the car is cold it starts fine. And if I put the car into gear and give it a small amount of gas right away, it is fine. BUT if I start the car then put it into gear while keeping my foot on the brake, it stutters and feels/sounds like it’s about to die. It never actually does, though.

Clogged fuel injectors? Or does anyone else have a better theory? Thanks!

Oh, and about 2 weeks ago, I ran out of gas for the 1st time ever. I could have sworn that I still had at least another gallon in the tank. (the low fuel light had come on, indicating 2 gallons left, but I had only driven 12ish miles since that happened) I don’t know if it is related, but figured I’d throw it in there.

Possibly. It could be many things that are just “a little bit off”. How is the routine maintenance? Has it been performed? Forgot?
Ok, start there. Change the air filter, fuel filter, spark plugs and wires, pcv valve. Put a bottle of fuel injector cleaner into the gas tank. If there’s still a problem, use a Throttle Body Cleaner on the inside of the throttle body, and the iac (idle air control) valve. Use an MAF (Mass Air Flow) Sensor Cleaner on the MAF. These are simple, easy, things for a novice mechanic to do.
If there is still a problem, come on back.

IT is not a good idea to run out of gas, it is not a good idea to run down to where the light comes on. It can be hard on the pump and could have been the reason for your problem. That said I would start with Hellokit’s suggestions.