I'm no expert, but the way I understand it is your rates won't increase because you were not at fault and can prove it.
Secondly, this asshole hit your car and ran, so fuck them, this is one time you maybe should talk to the police.
Another thing to consider is that filing this can make it show up that your car had an accident on your Carfax report in the future if you planned to sell the car. First thing I would do is go get a quote from a shop and see what the cost to repair will be, then go from there.