To keep your iPhone 3GS running its not a good idea to keep using the original battery it came with. Over time, the battery starts to lose its capacity and begins discharging quicker than before.
To avoid this and have a better battery life your iPhone, buying a replacement battery can be a good idea. As the iPhone’s don’t have an accessible back, the battery needs to be replaced by opening up the back. This needs tools and a certain level of expertise. Some of the batteries come with the required tools, while some don’t.