Braces can absolutely help your overbite, and if it is slight your orthodontist can definitely correct it. However, it sound more like you are concerned with the position of your jaw than the position of your teeth.
If you want to move your jaw forward you have a few options:
Orthognathic Surgery - This the most predictable way to correct your problem. The surgeon will do exactly what you are simulating by positioning your jaw forward, so you'll have a great idea of what the result will look like. Surgery is a big deal and expensive, but if it can improve your face dramatically it is definitely worth exploring.
Fixing your Overbite with Braces + Genioplasty - Another option would be to get your teeth to fit together and then going with a less invasive and less expensive surgery to position your chin in greater harmony with your face, and give the appearance of a longer jaw. Not everyone is a good candidate for a genioplasty, so you'll need to consult with a plastic surgeon to make sure the end result will look good (doing a genioplasty when orthognathic surgery is indicated doesn't turn out well many times).
Herbst Appliance - This is a forward mandibular positioning appliance. This treatment works best in growing adolescents, but it may be able position your lower jaw forward into a stable position as an adult (I wouldn't recommend it for really large jumps forward though). Your orthodontist will be able to tell you if this appliance is even an option for you.
It is great that you are already aware of your goals for treatment. Knowing what you want makes our job very easy since we just have to advise you on the best way to get you there.