Yes you will need insurance and smog certificate (unless you get a pre 1974 car, those are exempt) can't register the car without those. To do that you will need to visit out lovely department of motor vehicles
unless you are a big fan of waiting in long lines call ahead and make an appointment, also go in the middle of the week to avoid the crowd.
I presume an Aussie drivers license is good here but have no personal experience.
Check autotrader.com, ebay, or recycler.com for a car.