Car insurance question

Car insurance question

(Sorry if this has been asked recently, I only briefly skimmed the past car questions 'cause I'm at work trying to get this done, arrggh) SO I am switching off of my dad's car insurance policy (which I paid him for) to having my own policy in my own name and I am so confused by all of the monetary options for different things. Being a dad, my dad says, "THE MAXIMUM COVERAGE IS ALWAYS THE BEST." Yeah Dad, not when you're trying to save every penny possible! My question is: is selecting the highest coverage possible really worth it or can I go a level lower? Is there really a huge difference in my payment AND coverage if I choose 50K/100K versus 100K/300K? (FYI if it matters, I have a 2003 Honda Civic which is paid off, my commute is 6 miles and I park my car in a decent neighborhood. The car insurance company I am requesting the quote from is not debatable, it's a reliable company recommended by my friend in the insurance industry.) Thanks so much for your help!
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