Problems with 99 Plymouth/Dodge Neon?

Since I have had my car (which has only been for about 5 months) it has had problems starting but not every time it has the problem. When I start it, it turns over until it catches and then it is fine. Lately it has been happening just about every time I start it. Tonight though I was driving it and the engine turned off while I was pressing the gas. When trying to start the car again it would turn over but wouldn't catch. I've been told that it could be numerous things from my starter, to my spark plug, to my fuel injector, to my oil. Now I know I need to change my oil that is a given but is there anything else that it might be.