Oyster on line is loaded the following day so not much use for the occasional user, as is auto top up. I wouldnt know about topping up with phone but if on line takes a day to load up when does purchasing by phone load up?

Another link re visitors/oystercards/travelling with children (from TFL)
http://visitorshop.tfl.gov.uk/help-centre/travelling-with-children.html
This thread seems to have gone political and may not be answering much any longer.
Agree with the airbnb suggestion for a family. Some great apartments available. If you don't find anything central then somewhere like Kennington or Brixton in south London are close to where you'll want to go with good travel links.
Anyway - the only three London pieces of advice are all travel related
- Get an oyster/travelcard immediately
- Wait for people to get off the tube before getting on and stand to the side to let them do it
- Stand on the right on the escalator and walk on the left.
Follow that and you'll be richer and more popular. Enjoy.
Oh and when you are looking for the traditional pub - ignore the touristy Sherlock Holmes by Trafalgar Square on Northumberland Ave but go a street back to the Ship and Shovell in Craven Passage. Much better. And only 30 metres from Benjamin Franklin's house in London.