Hello Lily3.
Of the two places you have at the top of your area list, Notting Hill is a better choice. To that list, I'd also add Hammersmith/Chiswick for location, green spaces, family friendliness, and ease of commute to the best private schools.
Yes, there are the rumoured put-your-child's-name-in-the-womb places, but in reality, there is so much movement on those lists due to the transient nature of many Londoners and everyone always manages to get a spot at their desired schools. Additionally, some schools are assessment based at 3-4, so there is no need to feel pressured at this point.
In terms of searching for pre-schools, I'd do a simultaneous search (once you have decided on an area). In the areas you are looking, there are many, many lovely pre-schools and there is no need to worry about finding a spot in one. In terms of feeders, you are speaking more of nursery level and some of the schools you are looking at do have their own nurseries attached.
I am American, and I would not look at the American school if you are even thinking of your children staying on to go to University in the UK. Additionally, it would be better if your children attend local schools to assimilate to the community and their new home. It would also be better for you as social life tends to form around schools here, specifically primary schools.
You can start your children off at the same school, but many of the pushiest pre-preps (the ones with the best records of getting children into the top schools at the next level) seem to be single sex. Additionally, there is a disconnect in the English private system between the timetable for girls and for boys. Boys attend pre-prep until 7or 8 when they take the 7+/8+ for the top preps (Westminster Under School, Colet Court (St. Paul's Prep), Kings College Junior School), but girls will remain until 11. If you decide to keep your son at a prep which is not linked to a senior school, they will have to take pre-tests at 11 and Common Entrance at 13. Confusing, I know. No need to master the intricacies of the system yet, just have an idea of what is to come.
In terms of selection, most do it by first accepting siblings then by order the applications came in. Others will have an assessment where they are looking for teachability and fit of the children/parents with the school. In terms of fame wedging your way into a desirable school, not sure about this. Probably does help, but not in as blatent way as in LA/NYC.