I think ehBeth is still in insurance and I used to be. I think a few other folks work in the field. Neither Bethie nor I are/were in customer service, at least I don't think she is. But we've both adjusted claims, and I've worked in Legal. I've worked for AIG, AETNA, Liberty, Providence Washington (went bankrupt), Plymouth Rock (probably not available where you live), and I've had GEICO but never worked for them.
Keep in mind not every carrier is available in every state and sometimes you are dealing with a local agent for the most part, rather than the actual carrier.
We have Liberty Mutual, we had gotten them when I was working there and never got rid of 'em. I've liked them in terms of they have been good with claims which I think is the main point. I've gotten reasonable explanations if something is being denied and quick service for payments. The drive-through claims is good, you need an appointment but really just to assure that you don't have to wait. Prices are high, though -- GEICO was cheaper and it's been a long time since I used them but I do recall they were okay with claims, too. But I've only been in property damage-only accidents so I've never really had to test either carrier.
Every insurance carrier wants to take your money (premiums) and hold onto it for as long as possible (claims). This is how they make their money. I found this online, dunno how good it is:
http://www.leaseguide.com/Articles/autoinsurance.htm They do suggest looking at Consumer Reports and I think that's a good idea, too.