I use State Farm. Stay away fomr the small fly by night outfits, the consequences of not being properly backstopped in an incident are way too great.
Each state has minimum liability requirements that you MUST meet to be on the road. These will cover the other party if you are involved in an accident......fixing their car, fixing their injuries.
ETA: Having a GOOD insurance company will also help you if you are in an accident and the lawyers get involved. They will vigorously defend you. I smaller one may not have the resources to go to bat for you.
State minimum liability us what you have to have. I carry comprehensive and collision too. Comp covers the "act of God" stuff like hail damage and deer hits. Replaced two windshields in my truck too, one was a rock from a truck, the other was a friend who decided to try and fit a 4x12 guitar cab in my front seat. Over the years it also paid for hail damage on my truck, a deer hit, and a deer hit with my car that totaled it.
I started out with liability only at the age of 20, with American Family. It was $38 a month. After 12 months, it climbed a little at a time until I was paying almost $100. I never got any tickets or accidents, so I was like WTF? I went next door to the State Farm agent, got a quote that was half what I was paying, added the collision and comp coverage, and never looked back. State Farm is the best, and they have always been right there to take care of any of my claims. I currently pay $101 a month for full coverage/comp and collision on a truck and a car, and renters insurance with extra coverage for my gun collection and jewelry.