auto insurance company ? Today a vehicle is a very large investment. I would recommend finding a repair facility or facilities that you feel comfortable with and have confidence in ahead of time. This is where you ask family and friends for advice. Visit several repair facilities and ask who they prefer to work with to return your vehicle safely and properly to pre-accident condition.
The repair facility is the most important, not the insurance company. The shop actually repairs your vehicle, not the insurance company. They just pay, and guess what, they want it done cheap. The insurance company will try everything under the sun including almost demanding that you go to one of their shops. This is not always a bad thing, some reputable shops are a preferred provider for many insurance companies. You have the right to go to the shop of your choice in most cases unless your actual policy states otherwise. In most states, you do not have to pay more regardless of what the insurance company tells you. Ask an auto body repair facility and they will tell you.

