What serpentine belt is the correct one for my car, 03 GT? The GM # on the belt is 12578869. Is that the longer or shorter of the two belts listed for this car? Can I just buy the longer one from say NAPA and be ok?

That # looks right, not sure about any other size belts just the one and yes NAPA would have it.
Autozone is about $10 cheaper for the Good Year gatorback. Which is way better belt then the OEM GM belt. GM belts squeal and are just noisey constantly IMO.