If you have the optional collision coverage, insurance pays for collision damage to your auto, less any applicable deductible, no matter who causes the accident. If your car is financed, your lender may require this coverage and may require it to be fixed.
Why would you pay for this yourself? You were not at fault and not cited by law enforcement. Since the cost to repair this correctly will certainly exceed your $300.00 deductible, this is exactly what you have insurance for.
First you need to submit a claim to the insurance company with all the information you have. Then find a body shop you feel has a good reputation for quality work, get a formal written estimate and submit that to the insurance company as soon as you can. Don't just go to anyone they recommend.
I have had quality work done by Dick's Auto Body in Somerville, MA. They work on lots of BMWs, Porsches, and other high-end cars. Frank the Manager there can guide you correctly.