Can you provide me with some tips on finding a good car insurance company?

There are many insurance companies out there, and finding one won't be a problem. However, finding an insurance company is a serious matter and finding one that will suit your lifestyle and budget best is not easy. Here are some tips with finding a good car insurance company:

Shop online and compare a number of companies and rates at once. You'll save time and money this way, only if you do take the time to shop around and find a company that will work best for you.
 
Contact your local insurance agent. You might want to look for an independent agent who will be able to explain coverage and provide you with quotes from various companies. Ask for recommendations from people that you know - that's one way of finding an insurance agent.

Try purchasing insurance from a company that will sell directly to consumers - rather than through agents.

Keep in mind, that if it's your first car and you don't have a driving record, that won't play a neither positive nor negative effect on your car insurance rates and premiums.

If you don't have a credit score (a very low credit score), then that will always play negatively on your car insurance company.

Always keep in mind that other than friendly customer representatives, the financial strength of a company is always important.

Also, if you just purchased your first car, you should consider joining an auto club membership. This will give you a variety of discounts on gasoline, tickets to theaters, hotels, etc...

Asking about discounts never hurt anybody. You might benefit from multi-car or multi-driver discounts.

You might receive a multiple policy discount if you purchase your auto insurance through the exact same insurer that covers your renters or homeowners insurance.

Take the time to thoroughly compare multiple companies. Surf online and see what's out there. Talk to your friends, family, and co-workers and let them help you with finding a car insurance company.