Wow! That picture above is somewhat similar to what I had, but mine was worse. I had a "fang" (canine) on upper and lower teeth that stuck out way in front and above the other teeth. But my case was more severe, as there was no gap at all for that canine to move into, so basically my canine and lateral were right on top of eachother. And everything else was crooked and overlapped, too. Here's a photo of my original teeth. I think it makes my teeth look better than they really were:
If you have a canine that sticks out or up, be prepared for years of braces and devices. There is no easy fix for bringing a canine down a big distance. Cosmetic dentistry probably won't help either. My case was so bad that I needed 8 extractions, and no wonder! Glad to hear you think you have more space than I did, as that may avoid extractions and speed things along.
Also like to add that I completely understand what you wrote about your parents. Mine were the same - they had the money, they simply refused to help me look better. Even to this day, my parents NEVER saw getting braces as their responsibility. It was my problem and I had to accept the way I looked (even though every other kid I knew got braces and had great smiles afterwards). What a great message to send to your own child, that they aren't worth "fixing". And it hurts for a long time, as I am still bitter towards my parents sometimes.
Hope you find a great ortho and get on the way to the smile you want!

Debanded in May, 2006! Total sentence: Three years and two months. Now in hawleys which make me gag! Before braces, I had dracula fangs in their own rows, and everything else was crooked, crowded, with a cross-bite, too!