Since the gun must be transported unloaded, a lever gun is not ideal; they're slow to load. You want something magazine-fed, or at least something that can be fed by stripper clips. You
can keep loaded magazines in the car,
so long as they are not attached in ANY way to the firearm.
An SKS would be an good choice, especially since they're inexpensive. Of course, it must be CA-legal (fixed 10-round mag only, no grenade launcher). I wouldn't want to keep an AR in my vehicle, since many LEO don't understand the OLL situation (they're illegal by statute, and legal only by case law). The same is true with RAA Saigas and other off-list AK types.
An M1A or M1 Garand would work, but battle rifles may be a bit too much for urban situations (use frangible ammunition?) and I wouldn't want to store a $1500 rifle in my car.
The Kel-Tec Sub-2000 is a perfect "truck gun" but it's not legal in California.
But the SU-16CA would work well, I think... fold-able, .223, CA-legal, and magazine-fed.
A Ruger mini-14 or mini-30 would also do well, though IMO they should be more accurate for the price.
A semi-automatic shotgun that accepts a detachable magazine is an assault weapon. So, no Saiga shotguns.
Also beware of local laws... for example, Berkeley has a complete ban on semi-automatic long guns. BTW, I don't
think there's any destination requirement for pistols; the only difference is that pistols must be in a locked container (can be the trunk). See PC 12026.1.