If you have been involved in a collision that is not your fault, you have the option to go through your own insurance, or go through the other parties for resolution of the property damage.
You will have to get the other parties insurance information directly from them, or from the police report in order to file a claim. Often, it will likely take several days to obtain a copy of the police report, and their insurance is likely going to want to investigate or speak to their insured before they accept liability. This could potentially mean a delay in getting a rental car or getting your car fixed.
If you go through your insurance, there are several considerations such as, whether or not you have rental car coverage. If so, you may be able to get into a rental car quickly if needed.
Another consideration is whether or not you have a deductible on your policy. If so, you may have to pay the deductible up-front to have your property damage addressed. Ask your insurance company if they are willing to waive the deductible, or if they will compensate you for the deductible amount if they recover that amount from the other party.