Contractor first for an inspection, insurance second, because you want somebody who can document what actually happened before you open a claim. Take photos from the ground now, including the stain inside, with dates on them. On the storm chasers, the tell is that they knock on your door and want a signature the same day. Local companies do not work that way. We used Roofing & Siding of Cape Cod https://roofingandsidingofcapecod.com/ after a nor’easter and they tarped the slope within a day and wrote up the damage properly for the claim. Do not let anyone start permanent work before your adjuster has seen it. Keep receipts for anything you spend on emergency work, most policies cover reasonable steps taken to prevent further damage.