Typically, how much do permanent veneers cost?

I'm only 17, which is why this is so upsetting, and have a terrible history of bad teeth in my family. My Great Grandmother, Grandmother, Father, and Aunt have all had to have false teeth. I'm getting cavities left and right and I brush regularly, floss, and mouth wash. My dentists says that it's inevitable. It's a hereditary thing. I already have one tooth pulled, and every tooth around it now has a cavity so I need to get this fixed pronto. I brush at least three times a day, and even had my dentist put a protectant to stop this from happening, and nothing has helped. By 25, I will have false teeth. I would really like the kind that screw into your gums (not dentures) seeing as I am so young. About how much would that typically cost?