Commute to Fulham - where to live?

[WhereToLiveinLondon]

The commute will be my DD's - she will be going to school in Fulham in Sept. Haven't lived in London for a few years and am finding it hard to work out the trains! Where could we get maximum space/peace/greenery for a doable train journey for a young teen to West Brompton or tube to Fulham Broadway or Earls Court? We need 5 beds (extended family situation) and have a budget of 2-2.5m (same). Is St Margarets too far out? Big thanks for any suggestions.