<human>: Can you condense the text into a few key points?

I got 2 quotes from Geico for insurance, which are actually pretty good considering I am an 18 year old male. For me and my father with 3 vehicles (2 under his name, 1 under mine) it would be $260 with bodily injury or $160 no bodily injury. Our arrangement is that he currently pays $130 for his 2 cars (w/o bodily injury), so anything past $130 would be my responsibility. I would much rather spend $30 bucks for car insurance than $130. 

Our agent/broker told us "that it's best to have bodily injury because if for some reason I get into an accident and I am at fault, then they can sue me, and since I have nothing, they can go after my father and put a lean on his house". Is this legally possible? Now I'm not planning on getting in an accident, I'm a safe driver, but if for some reason I get into an accident and it was my fault, can they go after my fathers assets? Back when I did drivers ed I read about Florida being a no fault state. What does this mean in layman terms? Does this help or hurt my situation? 

Do I need to get the more expensive plan? I do not think I can afford the $130 a month, but I do not think a $100 difference is worth possibly losing/leaning a house over. 

The house is not in my name at all. My car is on my name.
<bot>: If my dad and I were on the same insurance and I got into an accident with my car can my dad be liable to pay damages including putting a lean on his home? Florida