Can i get cheap car insurance and still have adequate limits in the case of an accident?

Hello, i would like to ask you, if is possible to arrange the most affordable auto insurance policy while holding standard or above standard coverage limits in the case of traffic accident. I have compared different insurance companies including Progressive, State Farm, GEICO, USAA, Farmers and some smaller regional insurers, but in all cases the limits has been limited :) My primary question sounds somehow like this: is there a way to improve and increase my coverage limits and pay much less than presented by majority of insurance companies? If so, what should i do, where should i look and does this policies apply for all states in the United States? 

I know that liability and car insurance vary a lot

Of course i know, that insurance coverage limits vary by state, but  what are the most obvious / average prices for liability / car insurance in every US state? Are there some standard prices and info what is some "standard" limit? Thank you.

By the way, how much does the performance of my vehicle matter when considering buying better policy?