Had an 01 2500HD 6.0 that had fuel pump go out at 70K miles. Previous 00 1500 w/5.3 had fuel pump go as well. Dad's 01 1500 had his go at around 100K. Bottom line is GM fuel pumps seem to be the most problematic issue on those year trucks. I never experienced hard starting prior to the pumps going out. They just crapped out all of a sudden and the truck would get zero fuel pressure. Thats not to say yours isn't in need of replacing.
When is the last time you changed your fuel filter and how long do you typically go between changes? After talking to several dealers the consensus I got was to change the fuel filter every 10K miles and will help preserve the fuel pump.
I would start by putting on a fresh fuel filter. If your starting problem persists then replace the fuel pump. I changed it myself on my 01 2500HD by removing the truck bed. ITs not as bad as it sounds... Two adults can easily left the bed off and I believe there are ~8 bolts holding it on. CHanged in out in about 2hr.