I have a 1997 Chevy Cavalier 2.2L. Randomly it will turn over but not start. As long as I do not pump on the pedal (I learned the hard way that made it worse) and just turn the key off then try and restart, eventually it runs. It does idle, and it will idle for a long time if I let it sit for even 10 minutes, but the idle is rough/"sputterly". When I go to accelerate, initially or even after driving for an hour, the engine hesitates then suddenly it will accelerate. I learned to gently step on the pedal so it doesn't just suddenly accelerate quickly. When I come to a stop sign and then to a full stop it will randomly sputter and die quickly but then start right back up. After driving for a while and if it doesn't do what I previously stated then randomly, depending on how long I am at a stop light, it will do it. Otherwise it doesn't die but still hesitates to accelerate regardless. The fuel pump was replaced when I got it.
A code reading from Autozone read bank1 o2 sensor was bad and bank 2 o2 sensor bad with it either running rich OR running lean (different readings at different times) at the time with a misfire on piston 2. I replaced the upstream o2 sensor, air filter, and spark plugs (which had carbon but not excessive buildup).
A while later, with this problem still persisting, another Autozone code reading shows the bank2 o2 sensor still bad heatercoil or something (I am saving to replace it) and then showed the the engine was running Lean AND Rich. Immediately the autozone employee pointed to the gascap which did have a really bad seal. It was replaced and I now know that pressure builds up and its necessary for that gascap seal.
I have not gone back to do another reading. I have had friends say that it is the mass air flow, or vacuum leak, or plugs (new), or wires (fairly new), or fuel pump (replaced when bought), or catylitic converter?. I am at a loss when it comes to what I need to even start considering and would appreciate the help of you guys. I am doing this myself and need help. Thank you for your help and suggestions in advance.

 

Your car is having idle issues.
It is possibly a vaccum leak or the IAC could be malfunctioning. Then you have the issue with the acelleration being sporadic and that points to the throttle position sensor