Regarding cost, there really is no cheapest insurance company. You rate quotes will vary. A company that is inexpensive to you may be very expensive for me due to the numerous variables that companies use to calculate rates. And, don't equate cost with service. Progressive is known as a relatively inexpensive insurance provider, and I've had absolutely no problems with claim processing the few times I've needed it.
When comparing rates, make sure it's apples to apples and coverage should be equal among quotes. Get quotes until you can't bear to look at another one, then pull the trigger.