We are looking mainly at state schools, and I have come to understand there are selective state schools after children sit for the 11+ exams.
@EminSydney which part of London are you moving to?
Most state secondary schools are "comprehensive schools" meaning that they cater for all abilities.
A very small number of areas (e.g. Kent) have an old-fashioned system of selective "grammar schools" and "secondary modern schools", where all children sit the 11+ exam to determine which school they attend. Secondary modern schools can be considered less academic than conprehensive schools, because they don't have the full ability range.
Some areas that have mostly comprehensive schools may have a stand-alone grammar school that takes children from a wide area - known colloquially as a "super-selective" grammar school. SW London has some of these (e.g. Tiffin School). They are more competitive to get into,but as they take from a wide area (and many people don't like them on principle) they don't result in other local schools being less comprehensive. There are many excellent state comprehensive schools in London.
I'm just going to start by looking for a good school.
The Government's inspection service Ofsted defines schools as Outstanding, Good, 'Requires Improvement' or Inadequate. However their inslection process is controversial, and changes every few years, so its not always a reliable measure (and especially if the report is a few years old). This Government website can help you find info about specific schools: https://www.gov.uk/school-performance-tables
What does 9-4 (A-C) mean??
GCSE results are given on a scale of 1-9, with 9 being the highest, but its a relatively new system that replaces letters. The letters in brackets are an attempt at mapping between the two, but it doesn't look accurate. This article explains the mapping better: https://www.bbc.com/news/education-48993830
I know the UK school year starts in September. Which year would my son go to if he is 15 years old in Sept 2024?
It depends when his birthday is. If he will turn 15 after September 1st he will be in Year 10. If he will turn 16 after September 1st he will be in Year 11.
Are the years which they would study determined solely by age?
It's determined by date of birth rather than age.
Does a local state school have to take them in if we live in the area ...?
Only if they have a space. The best schools may be full. You will be able to specify up to 6 schools in order of preference, but if none of them have a space you will be allocated a space in a school that has one available.
Is it possible to start any time during the year at all?
Yes. This is called an "in year admission" and there will be information about the process on the local authority website.