@CrownCoats Look at Hampton Hill, TW12, near Fulwell Station. The 08.12 from Fulwell Station will get you to Victoria for 08.49, changing at Clapham Junction. (Times are longer off-peak, between 45m and an hour, depending on the connection).
It is on the doorstep to beautiful Bushy Park & Hampton Open Air Pool. You can walk/cycle to Kingston across the park. It has a nice high street with a Waitrose, community theatre, library, cafes, restaurants. There are lots more cafes and restaurants in nearby Teddington or Twickenham, both 20 mins walk or 5-10 mins by bus.
For secondary, if you get the location right (north of the high street) then you can be in catchment for all three of Waldegrave School (girls only), Turing House (mixed, with an admissions point in Fulwell), and Teddington School, which are all popular options. You will also be in catchment for the Tiffin Grammar schools (if your kids are very academic). There are private options nearby too (e.g. LEH, St. Catherines, Radnor House).
Local primary school children go to Hampton Hill Juniors or Stanley School. Catholic children go to St James'. For CofE there is St Marys & St Peters (SMSP).
It's a lovely area, with lots of activities for kids.