Hey marella31 couple of things you need to do before you can start hunting. Also these things might help you find places to hunt and what is or are legal means of take.
1) Have you taken a Hunter Safety course? This is required in California in order to buy a Hunting License. 2) Read the 2012 F&G regulations, you can read them off of the main site of SCH. There are a lot of rules in California, reading the regulations will help you from getting in a bad situation with the F&G. (It's much cheaper to know the regs)
If you are taking rabbits and squirrels the .22 and the 12 gauge both will work.
For me which one I would choose would depend on the terrain I would be hunting.