The manual will specify the recommended viscosity (like 5W-30 or 10W-30) and the type of oil (conventional, synthetic blend, or full synthetic). Using the wrong oil can damage your engine.
Without knowing the engine size, I cannot provide a definitive answer. If you don't have the owner's manual, you can often find a digital copy online by searching for "[Your Engine Size] 1998 Dodge Neon Owner's Manual." The engine size is usually printed on a sticker located in the engine bay.