starting hard

I just purchased my first suburban, and my first Chevy product. ( ford guy no longer )
the problem is my suburban if it sits overnight it needs to crank over quite a bit to get fired up, but once started and shut off it starts first try. When the truck is shut off i can hear the fuel pump run for a couple seconds and shut off. Do i need a new fuel pump? I'm thinking maybee it leaks slowly back into the tank and loses pressure over time and thats why it take so long to fire?
 
Thanks Andy

Your fuel pump is acting normally.  The fuel pump runs for about 1 1/2 seconds when the ignition key is turned on and again for the same time period when it is turned off.  Next time, try turning on the ignition key and then wait a couple of seconds before you engage the starter.  Give it a chance to pressure up the fuel system before you try to start it.  You may want to check your fuel filter and your fuel pressure regulator.

Thanks for the info. How big a job is the fuel pressure regulator? And where is it located?
 
Again thanks for the help
 
       Andy