I used Geico when I first moved to the US. It was fine for me. Now I'm with All State. They're fine too. I take out the maximum insurance for liability (the minimum is shockingly low). Like Canada02, I carry an umbrella policy of $2M just to cover myself.
As for a drivers license - I think the Canadian one is valid for 6 months, but if the move to the US is a semi-long-term one (1 year +) getting a California drivers license might be worth it. Be prepared to take a drivers test (both written and in car) and the hassles of dealing with the DMV.
To get one (a driver's license) you need to provide proof of why you're in the US. A student/work visa and your passport is sufficient. If you have a SSN, bring that too, if not, just be prepared to deal with DMV people who cannot problem solve unless the answer is one they've done 20 times during training.
I've never heard of a credit check being required to be insured. Perhaps that's unique for the company DFF goes with. Where in CA are you moving to?
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