I am surprised no one has mentioned delivering a Reservation of Rights letter with Proof of Loss form as the first order of business before jumping into the investigation - Look up Waiver and Estoppal.
Why would the neighbors be paid? Where is their insurable interest under the insured's policy? The guy with the burned hand has a Premises Med Pay claim but the insured has to be legally liable for any other payments. If it is proven that the insured committed a deliberate act, then the only one getting paid is the mortgage company.
This case sounds like a righteous fire with possible subro against the contractor who did the work or the maker of the cook top. This would be good news for the two neighbors.
As far as contents, a digital recorder is great - make a .wav file and burn it onto a cd. Also take LOTS of pictures. If it is a big fire in a nice neighborhood where there's a lot of stuff, get a digital camcorder and video the house, narrating it as you go. This can be made into a DVD but keep the tape, if it is a tape. Juries love pictures.
Don't try to get everything the same day. If this fire is big enough, you will make several trips to the scene. If you have some "restoration" company not known to you, this may be a case of justifiable homicide in the right precincts. Just remember you are hired by an insurance company to work a fire claim for a specific insured. If there is a question of additional liability claims, that is a decision for the insurance company to make. If the carrier wants you to work the neighbor's house and he has a liability claim and his son, who is a lawyer meets you at the scene, DON'T DO IT. If you do, check your E&O limits.
Also remember that Fire Marshals can really blow a C&O. They think they are on CSI and can come up with some real winners. Look for the low burn and remember that the laws of Physics still apply. Multiple points of origin mean stop what you are doing and call the carrier and advise them that this fire may be of incendiary origin and ask for further instructions. The decision to hire an independent C&O is theirs and they may want you to suspend until they can get him out there with you. If a fire was incendiary, I wanted to know it immediately, not at the end of the day.
Also remember, arson is easy to prove, what is hard to prove is who set it. Mail fraud is where you usually get them.