The styles are brand names which arose when yoga travelled to the west. At its root, yoga is just one practice, or better, a way of life.
I would look for something that describes itself as "hatha" yoga and also ask whether breathing exercises, or pranayamas are emphasized. Pranayama is very important for anxiety and depression.
You may hunt around a bit and find a place that feels good for you. Yoga, regardless of what names are attached to it, will help you a great deal.