First at fault accident, most likely both cars totaled, is there anything else I need to do?

Just got home after an at fault accident. I stopped at what I thought was a 4 way stop sign intersection. After I stopped, I went through the intersection thinking the intersection was clear and thought the other car was stopping at their stop sign. But they did not have a stop sign and my front and their front left side collided.

I'm going to assume both cars are totaled from the damage I saw. My cars entire front bumper was ripped off and looked like it damaged both headlights, hood, fenders, and pushed the front hood/fender back/up enough that the driver door was wedged shut. Their car looked like it had damage to the front left fender, wheel, and possibly have some axle/suspension/control arm damage.

Luckily no one was seriously injured. No glass shattering, no airbags deployed, no visible harm, most likely only whiplash. But I'll wait until adrenaline wears down for everyone. After the accident, the cars were able to be driven/moved to a side road. Cops showed up a few mins later. He gave me a ticket for failure to stop at an intersection and an exchange of information (time/place, DL #, Insurance policy #). The police called a tow truck and my car is now moved to a friend's mechanic yard for storage.

I know I need to submit a claim for my car for insurance to determine if it is totaled or what the repairs will be.

Do I need to do anything for the other party's car? I'm sure they submit a claim against me and I'll be getting a call asking for what happened. Is there anything I should/shouldn't do? One thing I didn't do was get good photo/videos of the scene/accident. I didn't record anything until after we moved our cars off the road and I only got a short video of the intersection and 1 photo of the car.

Anything else I'm missing? I'm sure my rates will go up when I renew/add a new vehicle to my claim.