tl;dr: Bring all your paperwork; maybe drive to LA; keep the car; get bank account, driver's license, US phone; ask the people at YYZ for how long immigration takes; rent for 6-12 months; figure out some health insurance before you step across the border.
Find out from your company when your health insurance (if any) starts. If they don't offer any, or if it only starts after your first day on the job, look into buying some kind of short-term policy. If you have to spend one night in the hospital in the US, without insurance, it wouldn't be weird to get a bill for US$5,000 or more. The company may be able to refer you to an insurance agent (in LA) for this.