I'm in the market for car insurance for the first time, and I'm trying to understand the best way to approach it. I've talked to some insurance salesmen, and they consistently try to convince me that I need a lot of coverage, in case I cause some big car accident (this is, after all, their job).
However, let's say for the sake of argument that the total value of all my assets is only around $30,000.
I believe that in this situation it's generally much cheaper to get the minimum amount of car insurance coverage allowed by law ($25,000 / $65,000 bodily injury and $15,000 property damage), and then to instead pay for personal liability insurance which covers an amount slightly greater than my assets. This type of insurance, in general, seems to be much cheaper than car insurance which covers a large amount of money.
My understanding is that, if I get in some accident my car insurance doesn't completely cover, the people involved may be able to sue me. However, assuming I don't disclose what type of insurance coverage I have, they are only going to try to sue me for "all I'm worth" (i.e., the approximate total of my assets). If this does occur, the cost will be absorbed via personal liability insurance.
Is my understanding of how this works correct? Do I really need a large amount of car insurance (the insurance salesmen seem to think that $100,000 / $300,000 bodily injury and $100,000 property damage is what I should buy)?