While State Farm's shopping experience is well-reviewed, customers did not feel as strongly about it's claims handling process. The company scored about the same as the other four large companies, but was still mediocre. A large national company may be expected to not be very efficient because of the various departments involved in handling individual claims. If you want the assurances guaranteed to you by a large, "legacy" carrier, then State Farm is the best to go with.
When you purchase comprehensive coverage, you will select a set deductible, which is the amount you pay out of pocket toward a covered claim. Let's say you choose a $500 deductible, and your car is later damaged by hail in a covered claim. If it costs $1,500 to repair your car, you would pay your $500 deductible, and your insurance would pay the remaining $1,000.