The insurance company should pay for any tree removal for a tree that hits a building.
I'd recommend a Stihl MS250 for an all around chain saw. It comes with a 16'' bar and is great for cutting 12" or smaller. It does bigger stuff, but a little slower. Buy a gallon of 40:1 premixed gasoline. [about $10]. For storage; pour out the old gas and fill with the $10 stuff and run it for a couple of minutes. It will last 1 to 2 years before the carb gums up. Also, buy the correct Stihl file/holder guide. It is cad plated flat steel with angle marks stamped into it. [.325, I think]. And an extra chain.