Yes, it is important to get a low-priced auto insurance policy so you can spend your hard-earned money on other things. 
Yes, it is vital you find the policy that best suits your needs. But what may be more important (and is a factor many people do not take into consideration when shopping for insurance) is that the company you choose is financially secure. If you're paying money for insurance, you want to rest assured that you're covered, and that your premium payments will ensure a timely payout if you ever find yourself with a serious claim. How would you feel if your insurance company told you they are in financial trouble and are unable to pay your claim? As much as we like to believe our insurance company is financially solid, and will be there for us in times of trouble, unfortunately, this is not always the case. Many people buy into the "bargain basement" mentality; they buy the lowest priced insurance they can find to keep more money in their pockets. Understandable, right? We all want to save a few dollars where we can, especially when purchasing an intangible product like insurance. But an unfortunate side effect of these "bargain basement" insurance companies is their lack of stability, and potential lack of available funds to pay claims when needed. Often one or two major claims can have serious financial consequences for a small financially strapped company, and the rest of their customers may find themselves in a difficult situation if they should get into trouble.
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