Be sure you get some quality training on firearm safety and see if you can find a way for your family to get some experience on the range with a number of firearms so you have some idea of which to chose. Gun owners who are range members are quite often very helpful and actually enjoy introducing others to the shooting sports. In many cases you may be surprised that a white range member is not racist in the least and would see no problem with helping your wife and son.
I remember many years ago I took a black co-worker to the range to show him what shooting a handgun was like. When we left I asked him what his opinion was. He told me that thing that impressed him the most was just how friendly the range master and the other shooters were and how well he had been treated. He joined the range and one day decided to take a concealed weapons course with a really good instructor who spent considerable range time before he would pass an individual and fired at targets placed at 75 feet to arms length. The instructor was so impressed that he tried to get my co-worker to get interested in competitive shooting events.
Unfortunately it sounds like you live in city where it may prove difficult if not impossible to obtain a concealed carry permit for a firearm as it is a "may issue" state.
California is a "may issue" state for permits to carry concealed guns. The willingness of issuing authorities in California ranges from No Issue in most urban areas to Shall Issue in rural counties. Additionally, the issuing authority can also impose restrictions on the CCW permit-holder, such as limiting concealed carry only to the purposes listed on the approved CCW permit application. However, concealed carry permits are valid statewide, regardless of where they were issued. This creates a situation where residents in presumptively No Issue locations such as Los Angeles and San Francisco cannot lawfully carry a concealed firearm, but residents from other counties with more permissive CCW issuance policies can lawfully carry within these same jurisdictions. California does not recognize concealed carry permits issued by other states, and non-residents are generally forbidden from obtaining a California concealed carry permit.
https://en.m.wikipedia.org/wiki/Gun_laws_in_California
The solution to that problem sounds fairly simply. Just get "shall issue" concealed carry passed in the state. The chances of that happening anytime in the near future is like my winning the LOTTO this week if I buy just one ticket.
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