When stopping the engine will stahl and when going the engine will go as long as you keep it over 1500 RPM's.The transmission is manual 5 speed it is an 05 neon srt 16 valve.

Could be timing or carb.Need more history

fastest car under $24,000. nice choice, sounds like a oxygen sensor. When these sensors get coated in in your exhaust manifold it creates a whole hoast of issues. Also check to make sure you dont have a valve cover leak. l know this sounds weird but if oil leaks in the spark plug wholes in your valve cover it will create arc jumping and can cause these problems.

you need to take it and have auto zone scan the computer for trouble codes on it,and id also check the fuel pressure on it,a bad tps sensor will cause it to not want to idle like that or the fuel pressure either one and the the tps helps determine how much gas the computer allow the engine to have so it could be related to the idle problem,if you have the scan done it will help find out whats going on with it,good luck.