Would veneers, lumineers, or bonding look best? (Photo)

You have an open bite, your best way to solve this is have a consult with orthodontist. If you do not want braces, and possible surgical intervention, see an expert cosmetic dentist to evaluate your teeth and your bite, and occlusion.
Dental bond in your situation can chip and break, lumineers is an option, you need to see waxup, the advantage no tooth structure removed! But cosmetically you might find it to be bulky, third option is porcelain veneer, but do not rush to any till you have done bite analysis!

Hi there.
Thank you for your question.
The difference between a bonding, a conventional veneer and a Lumineer is in the material used and the long term result. For bondings we use plastic composite materials versus veneers and Lumineers when we use porcelain materials. Therefore bondings can stain and don't last a long time.
The only benefit of the bonding is the lower cost.
The difference between conventional veneers and Lumineers is how much tooth will be shaved off your natural tooth. The other name of the Lumineers is "no prep" veneers which means that there is no significant shaving involved. If the tooth structure allows it the Lumineers are the best option - long term result, esthetics and minimally invasive.
In your case the best will be to get veneers  - especially if you already tried the bonding and teeth chipped again. 
When you schedule the consult with your dentist ask them for a digital smile design of your face so you can see what the final result will look like before you make a decision.
I hope this helps.
Best of luck to you,
Mina Levi

Hi:Since you already have an overbite, the best long term solution will be porcelain veneers.Best,Dr. Maddahi