If you have never done 3d work before, start simple. Tinkercad.com gives you a good way to do simple models, and there are a ton of tutorials. You can tinker other peoples models, to get an idea of how it works. Chrome.
From there, you can move to Fusion 360, which is a step up in learning curve. Again, many good tutorials and options.
As for 3d printing prototypes, yup. You can even get really good final prints inexpensively. If, however, you wish to mass produce products (100s of them) after you are satisfied the model is where you want it, you can move to injection molding.
If you only need 10, then you would still just get them 3d printed. Prototyping is a definition in flux right now as far as 3d printing goes. You can get great final prints with the standard and most used form of printing, FDM, which is both inexpensive and quick. Some hubs do a great job of printing final products with FDM. However, if your models are very complex, or you want the absolutely best quality available, you might want to go with another HQ method, such as SLS or SLA, which has longer delivery time, and is more expensive. But the prints are amazing.