As your policy price will often depend on the level of cover you choose to take out, it's important to decide whether you want to take out Comprehensive, Third Party, Fire and Theft, or Third Party cover. Being able to determine what type of cover is the best for you will help to speed up the comparison process and will make it easier to find a very cheap car insurance quote.
While laws vary from state to state, it's generally required that your teen have at least a learners permit before they can legally hit the road (with a licensed adult in the passenger seat). While they might not need their own insurance if they've only got a permit, it's wise to check with your insurer, just in case, to be sure of your local laws.
I was with Liberty Mutual for about 15 years and was very satisfied with their prices and service, although I never filed a claim. When I retired and moved from California to Florida, my auto rate went up a ridiculous amount, to almost $10,000 a year even though I had no accidents and one minor moving violation in the last ten years. On top of that, Liberty Mutual screwed up my umbrella policy and told me it was “unenforceable,” whatever that means, but I had to pay for the policy anyway up to the time I canceled and switched to Progressive, which cost about one third the cost of Liberty Mutual for an identical policy. Even good companies change over time.