If I have a product that I want to reproduce and eventually sell, when should I put a copyright on it? Should the copyright be immediately once I start publicizing it or can it be a little bit afterward and no one steal my idea?
Right away. You have a copyright immediately on creation of a piece of artwork, and labelling it will help your case down the way if someone infringes. There is no disadvantage to labelling it.
I'm assuming your asking of this question is indicative of your plans to make money on this. If that's the case, you should probably register the copyright as well. For something like $35, you can be sure that if someone does infringe, you'll have the necessary legal backing to stop them. If you choose to defer your registration until such a time when you want to bring someone to court for it, that fee raises to almost a thousand dollars. So it's definitely worth registering the copyright.
But yes, no matter what, you should certainly label your artwork as being under copyright.
In theory, your merchandise is protected under copyright the moment you create it as long as it meets all the requirements of a copyright. That being said, you need to make sure you have a way to prove when you made it. For example, my brother mailed himself one of his band's CD and didn't open it; the post-mark on the CD proves that it was create no later than that time. Of course, mailing yourself something is not a fool-proof method, and registering your merchandise is the most secure course of action.