The effectiveness of .22 against a zed is something of a debate. The whole ricochet around the inside of the skull thing doesn't happen that much, only 10 -20 % of the time.
Yes, it will penetrate the skull if it hits the temple, deadly triangle (the area around the eye sockets and nasal cavity) or the lower back of the skull. Chances of penetrating the skull in other areas can be increased by making sure the bullet hits dead on (otherwise the bullet glances off) and decreasing the range. That said the 10/22 fits all of your criteria and there are some other advantages to the 10/22 as a primary firearm in the SHTF scenario.
1) You can get 50rd Drum Mags for it.
2) When fitted with a suppressor it is very quiet. (although I'm not sure either of these legal in cali)
While we're on the subject I quite like this one: AWC Ultra II 10/22
Expensive, but nice.

1  out of 2 found this valuable. Do you find this valuable? Do you?    

Necropost, and the paintball/marble idiocy is debunked elsewhere. Locked.

 out of  found this valuable. Do you find this valuable?