So just to clarify OP
You apply through the borough where you live, both for schools in that borough and for schools in neighbouring boroughs.
You need to check individual schools admission criteria carefully, especially religious schools who often have their own very specific criteria which is nonnegotiable!
You do not need to already have a child at the school, though often in catchment siblings are given preference over other groups, including non catchment siblings. In smaller schools this can make it harder, though not Impossible for children without older siblings to get a place
Distance from a school is often a deciding factor , consider this when choosing your schools.
Use up all your preferences, only selecting one school is not a safe option.
List your preferences in the order you like them, but always include a local school which is your banker even if it is not among your favourites. If you don’t then if you are not offered any of your preferences you do not want to end up being offered a school you don’t want on the other side of your borough.
If your child is or has been a looked after child you will get priority, make sure you indicate this on the application.
If your child has special needs you need to make sure any supporting documentation is provided as required.
You are not making a choice, you are expressing a preference, many factors can alter the intake of a school from year to year, so unless you live next door to a school where you already have older children you can’t be sure of an allocation until allocation day.