Hi Chris!
I like to use every new concept I design as a unique character study, so I'm interested in seeing how you do with this!
In regards to feedback, it sounds like a good framework to build around. With a background as a police officer I would recommend you sample from the 'Earning the Badge' template from Tales from the 13th Precinct (pg.36), if you can manage it. Ghoulification sounds like an interesting perspective, and there are at least a couple Vampires in the city who have stomped around LA at some point (mine being one of them). While LA doesn't have an official site-canon Kindred society structure to it, you can take some liberties in the backstory.
Your history length can vary, but essentially you want to justify your character's mechanical design, touch on the life before and after the embrace, and provide a reason for arriving at Sacramento. It can be short and sweet or a page-worth. Mine ended up being around 500 words, which is on the long-side.
Once your character has made it through the approval process your immediate concern will be attempting to receive Acknowledgement by the head of your Clan or the Seneschal so you can feed without reprisals. There are several ways to go about it, but most often it is by attending one of the monthly Court threads held at Elysium. There's no guarantee that you'll receive Acknowledgement, and it will rely on IC interactions to make it happen. Failure to receive Acknowledgment doesn't mean you have to stop playing but it will make it very difficult to continue. After that it's up to you to find out who to talk to and how to further your character's goals.
That being said, since my Vampire, Konrad Roth, came from LA before he arrived at Sacramento. It's highly possible that they might have met in the last 10 years. If you want to shoot some ideas around about those circumstances, shoot me a PM with your idea and maybe we can get the ST to approve it. That would perhaps provide you a contact in the city.