Engine Stalls Then Rotates but wont start for a few min

I have recently bought a used '97 rs camaro v6 it ran fine test driving it and for the first few months. It only has 75 thousand miles on it when I bought it. But lately I have been having the car stall try to start didn't hear the fuel pump prime then wait a few mine and it will fire right up and continue on. Took it in spent $75 bucks on diagnosis and they said fuel pump they wanted about $1,000 bucks for fixes so I say no. Take it some whereelse fore cheaper.(Brought my own fuel pump and filter) get it fix runs fine on the way home. After work the next day take it out for a spin. Dies same crap but this time I hear it priming and everything. Took the car in to the ppl who installed it paid them $53 bucks for their diagnosis and they say they can't find it. I've read forum after fourm and I have a few ideas but I need to really need to get this solved. Rpm is always different can die at a stop sign, stepin on the gas or with cruise control set going 40. Someone help me.

Beavis