Car Insurance

Lately I've been saving up for a down payment on a new car because I'm wanting a car that is good on gas. So I've been putting money away from my checking to my savings account. Well it has been nice but what I'm worried about is that when I get a new car that my insurance will go up traumatically from what it is now. I know that I don't have any points on my license nor do I have anything on my insurance to have to worry about. But I'm still looking around to see what kind of insurance quote I can get before I purchase a new car. Now the only other thing that I have to worry about is what kind of vehicle to get!