All insurance companies are different with different rules but the majority rate based on risk. What does that mean? It simply means how much of a risk will you be to the company. Insurance is for profit so if you will have a higher risk of submitting a claim they will charge you more. Simple idea but very detailed in how they figure out your risk class.
Here is an incomplete list of risks everyone looks at
Previous insurance limits Lapse of coverage if any and for how long The actual limits you are buying (Higher is better, example Full coverage) Your personal credit score Any existing accidents / violations Crime area around your garaging address (where you car is parked when you are sleeping) Home owner VS Renter Other policies with the same agency (Home, Life, Inland Marine, etc) Your vehicles. How much does it cost to repair? How much damage will they do to others or property. Are they high end VS low end vehicles?
You are doing the right thing by shopping around. It costs nothing to get a quote other than a chance of slightly reducing your credit score. Like mentioned earlier your credit history is sometimes ordered when quoting someone. It probably will be ordered when you buy the policy. The more times someone reviews your credit history the more chance you have of your score slightly dropping. But honestly don't worry about that. Find who is the cheapest and go with that. Also get all of your insurance through one agent. You get discounts for bundling policies together.
My personal auto policy is 3 vehicles, 2 drivers, full coverage on everything. I've totaled a car last year and the other driver has a clean record. I live in the ghetto. My credit score is 815 and the other driver has almost no credit history. I've been with the same agent since I was 16. I have a homeowner policy and Inland Marine policy through the same agent. I've had zero lapse in coverage and never paid a late bill. I pay $200 a month for auto insurance. Your results may vary.
Good luck