1997 Chevy Cavalier `1997 chevy cavalier hard to start and

I bout this used car about a couple months ago and it ran nice. I had to replace a few things like a new mufflor because it had a hole in it and the alternator went bad so i replaced it with a used one. Nowadays she is hard to start in the mornings. It turns over like it wants to start, then it just shuts down. It usually takes a couple minutes to get her goin and once its on she starts up fine throughout the day. Also usually within the first few seconds of driving it the enigine stalls and wont move any faster even when i floor it. This occurs everytime i attempt to pull away and drive after starting it and usually stops after a few mins of driving and drives nice.