Any normal handgun is fine as long as your magazines are 10-rounds or less. Don't worry about the approved gun roster or anything like that, that only applies to buying a gun in California from a dealer. I would stick to a handgun personally but you could bring a shotgun. I'd personally avoid bringing any type of AR/AK pattern rifle. You'd be good to go with a lever action. Those aren't considered assault weapons...yet...and you can even have more than a 10 round capacity for those because they have a tubular magazine.
And be sure you're transporting it legally:
"Pursuant to California Penal Code section 25610, a United States citizen over 18 years of age who is not prohibited from firearm possession, and who resides or is temporarily in California, may transport by motor vehicle any handgun provided it is unloaded and locked in the vehicle’s trunk or in a locked container. Furthermore, the handgun must be carried directly to or from any motor vehicle for any lawful purpose and, while being carried must be contained within a locked container.
Pursuant to California Penal Code section 16850, the term "locked container" means a secure container that is fully enclosed and locked by a padlock, key lock, combination lock, or similar locking device. This includes the trunk of a motor vehicle, but does not include the utility or glove compartment."
https://oag.ca.gov/firearms/travel