There's a 10 day waiting period for all rifles, shotguns, and handguns in California. You can't just walk in, buy one, and leave with it. Gun shows have the same rules. Actually, you can't even legally sell one to a friend without going through an FFL holder and waiting the 10 day period. And yes, you have to pay for it at time of sale, not when you pick it up.
Handguns also require a Handgun Safety Certificate, a loading/unloading test with the firearm being purchased, and a utility bill listing your current residence. Even black powder revolvers fall into this category.
Oh, and that federal assault weapons ban being dropped doesn't make a difference in California because they have their own state law banning them that's enforced. You can't even legally import one even if you're permanently moving here from another state.