Lots of people will recommend an insurance company, but many of those are recommending it based on how low they quoted, not how the person was handled when they needed the insurance. Many have not needed to make or defend a claim. I have had four claims go through and am now a firm customer of A-Plan (a broker) who actually have branches that you can go and talk to a person in. That said, they have two branches within 18 miles of where I live, so that helps.
On the quotes. Check how unreasonable they are by playing with what you input. It would be wrong to lie when taking out the insurance, but using the electronic quote system to figure out what aspects of your details influence your quote should be fine. For instance, you could try different models and years of car, you may have one which is considered high risk. My mum was told that her Volvo 240 was not a high insurance group because it was fast, desirable or easy to steal, but because it would do a lot of damage if it simply rolled down a hill and hit another car! Insurance is affected by where you live, where you park, what mileage you do, what the vehicle is used for, your job, and the vehicle itself. Age has some bearing, but a lot less than it used to. Play around and find out why your quote is high, it may be something you can do something to change.
On dealing with the incident, keep written records of every letter and phone call you have with the insurance company. Names, dates, what was discussed, write it all down. If you have legal assistance through the insurance, don't assume that they talk to the insurance people, you may get asked the same things by different people who don't communicate between each other. Providing more details isn't always better, be clear, be concise, don't hang yourself by providing excess information.
Last time a guy "touched" my car it didn't look like he had done any damage, no cracks in the back bumper where he shunted me while I was waiting at a T-junction...however, he hit hard enough that the next time I opened my boot I could not get it to close again, he had bent the frame enough that the catch would not engage!
Your insurance company is not your friend. Whether the insurance companies agree that his claim is valid and needs to be paid, or not, your premium will go up because a claim has been made. My premium went up both times I was rear ended while waiting at junctions, there was never any question of blame, didn't matter that it wan't my fault.