Hesitation Chevrolet Silverado, 4.8L, 1999. Starts okay. Transmission in gear, engine hesitates for 10 seconds and up to 1 minute. Let idle and it clears up. If you stop motor, it may do it again. After clear up, it runs fine until you stop motor again. Fuel pump has been replaced, symptoms still the same. Test pressure on pump, all okay. 180,000 km.

Replace your crank angle sensor.

I had the same symptoms. First off, how long since you have replaced the spark plugs and wires? I know they are supposed to be 100,000 mile life but not in my case. Here is what I did to correct my issue (note: it did not do it all the time, only occasionally and seemed worse when it is cool in the mornings)
1. Replaced Spark plugs, the issue got better but did not go away.
2. Took throttle body off of truck and cleaned all the carbon from around the buttefly with toothbrush and carb cleaner. Took idle control module out as well and cleaned carbon as well, issue got even better but did not go away.
3. Replaced GM spark plug wires, only 55,000 miles on them, one at a time (just to determine which one was causing the issue if it was a plug wire). Cylinder number 6 wire was bad. So, replaced plug wires and wa-lah, problem solved. Not saying that is your issue, but it corrected mine.
4. While I was at it, I replaced O2 sensors b/c I did have one that was lazy according to the computer.
Truck now has 231,000 + miles and runs like a champ.