Moving to LA from UK with young family (Los Angeles)

My husband is close to being offered a job in Los Angeles and he’s successful we will be moving as a family early in the New Year. They want him to start Jan/Feb.
We have a 5 year old boy, 4 year old girl and a 4 month old baby boy so its going to be a big upheaval involving schools as well as a place to live.
From my initial research and trying to figure out where we want to live, budget and quality of life etc my impressions of Santa Monica/Sherman Oaks/Brentwood/Palos Verdes Estates and possibly Pasadena are good family locations with some great schools, although I’m aware can be expensive too!
I think my purpose for joining this blog is to ask anyone who has moved from the UK to LA with a family to offer me any advice or tips when it comes to choosing the right area to live and the right schools. We will initially rent a property in order to check out the surrounding areas before we necessarily commit however I obviously need to make the right decision re schools for my kids sake. I've also been advised to go for an expat neighbourhoods while we find our feet…has anyone got any views on this? If so, can you recommend any?
If anyone has any recommendations of neighbourhoods or schools in those areas or anywhere they think I should avoid (apart from the obvious ‘no go areas’ ive read about) I’d be most grateful.
This is all so new to me and so I’m trying to gather as much useful info as possible while keeping an open mind to enable me to make an informed decision…. Can you help??