1997 Chevy Lumina Starting and Acceleration Problems

I recently bought a 97 lumina 3.1V6 and after a couple weeks now, when I try starting the car it turns over like it's going to start but doesn't, if I turn the key off and right back to start, most of the time it cranks with no hesitation. (Sometimes a third time is required). When I go to crank it though if I just turn the ignition on for a few seconds and repeat a couple times then it will start right up so I doubt it's anything to do with my starter. I've replaced the plugs, wires, fuel filter, and now have a fuel pump ordered. I'm really not sure as to where to go from here if pump doesn't work. Also for a week now, sometimes when I accelerate it acts like im barely pressing the gas, doesnt matter if I have the pedal all the way down or not, then after a little while it starts accelerating just fine.