First, you're going to want to make sure that you know what you want. Since each car is going to change the car insurance rate, you're going to want to make sure that you're getting the best car for you, and your wallet. Just because your car is paid off, doesn't mean that you're going to be set for the next few years. You're always going to have to pay insurance.
Know your terms - Insurance can be confusing for anyone, no matter how many times you've had a rate come to you. Make sure you know how much you want to deduct, as well as how much liability insurance you want, and more. You're going to find that the higher your deductibles, and comprehensives are, the less you're going to pay on your monthly premiums. But, remember that if you get into an accident, you're going to have to pay more.
My word of advice to anyone is that you're going to want to explore at least 5-10 insurance companies. There are a lot of them out there. Your best bet is to find an insurance search engine out there that does the work for you, and go from there. What you're going to find out is that if you get 10 different quotes, you're going to get the best rate possible for your car.