Hard start when warm, bouncing idle after start?

When the car has sat all night in the garage. It will start easier with a little flutter on the gas pedal. Then the idle will bounce(between 800 rpm and 1300 rpm) for a bit then steady out. When the car is warm it takes more fluttering of the gas pedal then I have to keep on the gas to keep it from dying. If I lay off the gas after it starts it will die. After it starts and I get past the "bouncing point" it runs fine. I get 28+ mpg, the acceleration is smooth and strong. Two days ago I was waiting for someone, so I parked the car and just let it idle while I waited. Twenty minutes into the wait the idle was running steady at just under 1000, then it dipped between 500 and 300. It almost died with the dip in rpm's, then it when back to idling, and has not done it since. I was thinking it was the fuel pump but now after doing some reading I don't think it is. Any help would be greatly appreciated. Thank you!