There are worse states than California, but not many.
No one cares about the FFL paperwork from your original purchase. You don't need any. There is no proof of ownership paperwork. There is no "Registration" in CA except for "Registered Assault Weapons." You are not permitted to bring any "Assault Weapons" into the state so you won't be registering any.
Assault Weapons are defined by features or by those listed in the original law when it was passed. See the Assault Weapons flow chart below.
Handguns imported by those moving into the state need to be reported (
http://ag.ca.gov/firearms/forms/pdf/ab991frm.pdf) within 60 days but they don't have to be on the approved list.
http://www.calguns.net/calgunforum/index.php
http://wiki.calgunsfoundation.org/index.php/Main_Page
http://calnra.com/cgi-bin/flowchart.cgi
http://www.calguns.net/caawid/hgflowchart.pdf
There is a List of Handguns approved for sale but it only applies to handguns sold by dealers, not to possession or bringing into the state. As long as a gun is not an "Assault Weapon" private sales of non-approved handguns are permitted. Private (Person to Person Transfers) sales have to be done with the assistance of an FFL and a 10 day waiting period. C&R
long guns (older than 50 years) can be sold without the need of FFL or waiting period.
You must have a HSC, Handgun Safety Certificate to buy a handgun but it's a 6th grade level test, (be embarrassed if you fail!) but you can take it over until you pass. $25 at any FFL dealer for the test and it's good for 5 years.
There is no Approved List of long guns, they just can't have "evil" features.
You can't have magazines of greater than 10 round capacity unless you owned them before 2000 and have been living in CA since then. Can't bring them with you when you move here.
CA DOJ Bureau of Firearms FAQ
http://ag.ca.gov/firearms/pubfaqs.php
26. I am moving into California and I own several handguns. What are the new-resident registration requirements?
You are considered to be a personal handgun importer as defined by California law. You may bring all of your otherwise California-legal firearms with you, but you must report all of your handguns to the DOJ within 60 days as required utilizing the New Resident Handgun Ownership Report. You are not required to report rifles or shotguns. You may not bring ammunition feeding devices with a capacity greater than ten rounds, machineguns, or assault weapons into California.
(PC sections 12001(n), 12072(f)(2))
27. How do I know if my firearms need to be registered?
There is no firearm registration requirement in California except for assault weapon owners and personal handgun importers. However, you may submit a Firearm Ownership Record to the DOJ for any firearm you own. Having a Firearm Ownership Record on file with the DOJ may help in the return of your firearm if it is lost or stolen. With very few and specific exceptions, all firearm transactions must be conducted through a firearms dealer.
CalGuns.net is a great resource for learning about CA gun law.