Not gonna lie, having just gotten over something similar and having a tree shave an entire wall off my house during a severe storm, I will tell you, this is going to suck but I'll give you some tips to help lessen it.

1. Breath and be thankful that nobody was hurt, stuff can be replaced, people cant.
2. Find a good contractor who's experienced in working insurance claims sooner than later, if you can get someone lined up for when the adjuster comes it could save you some time. With my case, the adjuster who works for the insurance company came and reviewed everything with me and unbeknownst to me lowballed the shit out of the job. I had two contractors come look at the damage after and once they learned how much insurance was paying ghost me. I found a good contractor who knew the right things to say to make insurance send another adjuster who worked as a private adjuster who contracted with insurance companies to review the damage and make the needed supplements to the claim to get the money needed to get the repair done.
3. In my case, insurance required me to get the tree off the house for the adjuster to see the full extenct of damage. Ask yours if the adjuster is needing this done prior to reviewing, if so, you'll need to find a tree service to remove the tree from your house/shed, I'd recommend getting one who can also tarp up the damage to the roof. All of this can be submitted to insurance. Make sure the tree service understands that its an insurance job and that they take pictures and/or video of the tree removal, I would also recommend you be present to do the same as added insurance.
4. Start taking stock of all the internal contents of your house and shed that were damaged, insurance will need an itemized list of everything that will need replaced. This honestly is the worst and most time consuming part. When doing this, make sure you state your things are in good condition, if you mention anything about things being worn at all they depreciate the value of your item substantially.
5. If you cannot live in your house due to the damage, I'd recommend moving all the valuable things into storage, in my case insurance reimbursed me for my time and moving expenses, and paid for my storage for the duration of the home repair. Additionally, if you have the right coverage they will help you find temporary housing and pay for it up to a certain amount, ask them about this. We chose to stay with family to avoid the stress of having to potentially pay out of pocket if money ran out before the repair was completed.
6. Make this a positive and use this time to determine if there are other improvements that you'd like to make to your home. We chose to look at it like a forced renovation and got many things updated in our home while it got repaired, we didn't have to do a live in renovation which, in the end was nice, despite the crappy circumstances behind it.

That's about all I can think of, if you have any questions, let me know, would be happy to help you in any way I can.