I'm from the UK but have lived in LA for a decade - and the school system here is CONFUSING. I believe that if you live within LAUSD, you will automatically be given a space at whatever your assigned "resident school" is (there's an LAUSD resident school identifier where you enter your address and it will tell you what your resident school is). Whether or not you like that school is another issue... Then you can also apply to charter schools, which it looks like you've been investigating! (There are also gifted and magnet programs which you apply for differently as well, just to make things more confusing.)
As pp said schools in Santa Monica (which is it's own city, so not part of LAUSD) are generally thought to be good. In reference to the schools you listed, I don't know anything about Goethe or WISH so can't comment. People RAVE about Larchmont, and it's massively oversubscribed. However, as it's a lottery, you may as well apply and see if you get lucky! The main campus is lovely, and the lunches there are allegedly delicious if that sort of thing matters.
My own kid is in kinder at a CWC school (but not Mar Vista, as we're on the Eastside). She is loving it. Student and teachers seem dedicated and enthusiastic, great community feel, specialist art and music classes for all, and excellent and varied after school clubs. Traffic at drop off is a nightmare, but otherwise I honestly couldn't be happier with her experience so far.
The main problem you might have with the charter schools is that the lottery system is weighted -- for Larchmont and CWC I believe they give top preference to LAUSD residents. Which means you can live anywhere within LAUSD boundaries and be treated equally for this, but I imagine you're going to be low down on the wait list if you apply before you are resident in LAUSD... Which doesn't make it impossible, but imagine chances would go up hugely when you are resident within LAUSD. There is a lot of movement within the schools, so even if a place is not available immediately, people seem to get charter school offers as the school year starts...
I found the lottery system slightly terrifying, but we did end up with a place we are very happy with. Good luck!