Awhile back I called my insurance company and asked about insuring a new Ford 150, expecting them to say it's very expensive due to the aluminum now used. But I was surprised when they told me the price; it was about what I'm paying now on a Chevy truck. I asked why so (relatively) low, and they said because of the trucks 5 star safety rating and other factors.
As for raising your rates after an accident, I found that to be true if the accident is your fault. My wife was hit by someone running a red light recently, and it totaled her Mazda. The insurance company gave us a fair price for the totaled Mazda, and our rates didn't increase. But once I backed into a pole, damaged my bumper, reported it to the insurance company, and then they did raise my rates.
Lots of factors to consider.